It's good to see that the KPD of this timeline is not tainted with the fatuous indifference to the prospect of Nazi takeover shown OTL, summarized by Thällman's infamous line, "After Hitler--us!"
The dark side of Sverdlov's epiphany regarding the priority that had to be given to beating Hitler is of course that he doesn't recognize the viperous danger that the Nazi Party, and Hitler himself, pose in their own right--he merely sees them as the latest front of capitalist rule--which is not too far from how Stalin saw them OTL. The only thing special about a Nazi takeover in Germany from Sverdlov's point of view is that Germany might be permitted to arm itself, provided those arms were turned eastward against the Soviet Union--thus, the capitalists gain a whole new army devoted solely (on Sverdlov's theory) to attacking the Worker's State--one that the other established Entente powers might discreetly support as needed while maintaining some level of plausible deniability of complicity with German aggression eastward (against the criticism of their own left-wing elements in the populace). If the Germans in this scenario do well, the Soviet Union is discredited as well as being mortally mauled; then the Entente capitalist leadership can step forward openly about their support for the anti-Red crusade and count on the pro-Soviet elements of their own peoples to be demoralized and diminished enough to be managed by repressive measures. If on the other hand the German assault is countered and stalemated, from the Entente powers' point of view German lives and treasure are expendable, whereas if the Red Army actually gets the upper hand and threatens to start seizing German (or any other nation's) soil the Entente might come forth then as protectors of national sovereignty and freedom against the Red hordes, again defusing populist outrage.
If we wonder, "what populist outrage?" well, rather than trying to prove the Soviet Union had many friends, let me just reiterate this is
Sverdlov's thinking. As a Bolshevik and leader of the Third International, he believes, or anyway wants to believe, that large numbers of the Western working classes are either on the verge of revolutionary consciousness or in the vanguard already aware--that the tinder of the working classes of the developed capitalist nations must be near-ready to burst into red flame, as it after all was in Russia, as after all Red coups had occurred in Europe in the aftermath of the Great war--and these working class people are suffering the doldrums of the Great Depression too. It doesn't have to be objectively true for the Bolshevik leadership to still believe it--and I think that yes, the Communists did have some friends in the West in this period OTL.
So Sverdlov probably sees Western politics in general as a charade meant to by various turns mollify or intimidate the working classes into a lessened sense of class conciousness.
Now if the Kremlin troika had taken complete leave of their senses regarding the actual "correlation of power" in Germany, they'd have pushed for the KPD to try for a coup. Since they aren't doing that they have to be aware that there simply isn't sufficiently broad popular support in Germany for them to win--certainly not considering the almost inevitable reaction of France and Britain against any such worker's revolt.
If there were no imminent threat of a dangerous form of right-wing authoritarian takeover, it might make sense for the KPD to remain aloof of effective engagement in the machinery of the bourgeois state, maintaining revolutionary purity. Note I said "effective" engagement; OTL the German Communists were not such purists as to ignore electoral politics of course; they had significant numbers in the Reichstag--but they did not enter into effective coalitions with other parties (there being only one party they reasonably could have done so with, the SD) and participate in government on capitalist terms. Their electoral work was mainly a means of rallying support for their revolutionary program by demonstrating their strength in numbers--and also had effects on the decisions taken by the other parties that did involve themselves in political wheeling and dealing. And they could vote on items on the agenda of course, and even exercise the other parliamentary rights of legislators. But by refusing to make deals while Germany remained a capitalist, bourgeois state and society, they raised the banner of the transformed future world they fought for. This was a perfectly viable tack (provided that a lot of working people really did place their hope in radical transformation, and that there were prospects of increasing the number of workers who did so) as long as Germany remained essentially liberal--as long as the Communist Party had a right to maintain its organization, hold meetings, hold rallies, etc. If Germany were to go Fascist along Italian lines, the Party would be driven underground; if they were not able to prevent this by fighting, they could only be effective by subversion, and would be organizationally decimated since the best comrades would be those who were publicly known as Communists, and thus targeted by the new regime.
This risk was understood OTL too; the difference is that Sverdlov is looking ahead, five to ten years down the line, when fascist Germany might be used as a weapon against the USSR. OTL the Stalinist line was that there was little difference between liberal, even moderate socialist, parties and outright fascists, because all were committed to maintain capitalism and capitalism was on one hand an implacable foe of the worker's revolution--but on the other hand, doomed by inevitable historical evolution, in the form of inexorable growth of revolutionary class consciousness of the working class. Any bourgeois regime would inevitably leave working people with irreconcilable grievances that leave them just one way out--revolution. The fact that fascist forms of bourgeois society would decimate open forms of class organization would be offset by sharpening the conflict, and in the end since the working people are not only the majority but also the producers of all wealth and increasingly (as capitalist competition polarizes all society into a handful of owners and proletarianizes even the former middle classes) places the levers of social organization in the hands of those with "nothing to lose but their chains." Hence Thällman's OTL confidence that the Nazi regime would be short-lived and the final step that would prepare a sufficiently large number of Germans to either become committed Communists or anyway look to a Communist takeover with hope.
For the Communists then to turn to actively supporting and maintaining the machinery of a bourgeois society would be a betrayal of their credentials as the vanguard of the people's revolution; it could be justified only if there was reason to think that the fascist turn could form a third way, one that could strike effectively at the process of rising revolutionary consciousness and reverse it.
Here Sverdlov does believe this is possible--but he only thinks it is because the capitalists of Western Europe as a whole will be using the Nazis as a front to cover their cynical ploy to craft Germany into an anti-Soviet weapon, not because he foresees or understands how deep the control of German society the Nazis can manage on their own.
I've often wondered if a Red-Red alliance of KPD and SD could have stopped Hitler's bid for power, and generally assumed it would, based on the numbers the two parties together held in the Reichstag. OTL the Nazi Party actually lost ground in the last election held; I believe that they had reached their limit in terms of numbers of people who would actually commit to their extremist, illiberal program without reservations, and it fell short of the number who would remain committed to Marxism.
What happened here ITTL then is I suppose, that although Thällman could see the need urged on him by the Kremlin to make a truce with other Marxists who had taken a more reformist road, neither he nor the Soviet troika leadership understood the need to go beyond that and extend the truce to a significant number of liberal bourgeois as well. If for instance the strategy had been to persuade the Catholic Centre that they needed the Reds to maintain a balanced system but that the Nazis were too dangerous to work with, the resulting coalition would have been unstoppable. This particular constellation would probably be absurd since the Centre would have more obvious reason to fear Communists than Nazis (not having foresight as to what the latter could and would do, and knowing what Communists were potentially capable of, and often boasted of planning to do). But I guess, when I figure that an SD-KPD coalition would maintain its numbers in elections and govern on its own, I also figure that the coalition does reach out to key capitalist figures and put forth a program that maintains essential liberal institutions in principle, holding out hope among the more progressive industrialists that the radical program will be limited to reforms that can also strengthen German industry, in the context of the emergency of the Depression, and that other German voters who do prefer a liberal order will see the Marxists as being properly committed to maintaining a liberal order, for the moment.
This very obviously did not happen here. It is not clear to me how much the rise in votes for Nazis is supposed to be a simple reaction in fear of a reunified radical Left, how much it is supposed to be a response to clever Nazi propaganda (mentioned in the post, but surely they did their best OTL as well, with caricatures of Stalin in Sverdlov's place, and yet did not gain numbers for it) and how much it is due to Thällman or even enthusiastic SDs saying or doing things that reinforce the fear of the Left.
I suppose the next post will clarify how the Marxist coalition deals with the upcoming Nazi repression.
I certainly do think it makes a difference in the history and perception of Communists ITTL that when the crisis came, they did try to fight to preserve a liberal society against rightist repression. If we get an edition of the Spanish Civil War here, quite conceivably Soviet aid to the Republican side might be more effective in that the Soviets might do more coalition building and be less insistent on taking control, and that might tip the balance against Franco and result in a pro-Soviet, leftist Spain. There might also be more traction for Popular Front sentiment in the West against Hitler's later schemes such as the takeover of Czechoslovakia--perhaps not enough to derail a betrayal along the lines of Munich OTL.
However--bear in mind the exact nature of Sverdlov's apprehensions about Hitler--he doesn't see Hitler as being capable of taking over Germany in his own right, only as the catspaw of a shadowy international conspiracy of capital. Thus in subsequent years he is going to be blaming the leadership of the very liberal states he could hope to form a Popular Front with; it would be futile, probably, to persuade them to drop the tool they have forged against the Soviet Union. Instead I suppose the appeal will be to rival parties with leftist credentials to toss out their corrupt rightist leadership, or anyway watch what they do. Naturally people like Baldwin or Neville Chamberlin will resent the insinuation that Hitler is somehow "theirs!"