Imo people dramatically underestimate just how constrained Russia is by its neighbors and how bad its geographic position for threatening British interests is, up until the 1950s at the least. Germany's position has its shortcomings, but in the immediate following decades after WW1 it is far less crippling than Russia's.
Specifically, let's think of what the maximalist extent of Russian victory in WW1 is, and what the maximalist extent of German victory in WW1 is. If Russia won utterly and decisively - and this is a purely maximalist extent and has no reference to actual Russian war plans and war goals - then they can hope to carve off massive chunks off of Eastern Germany and Austria-Hungary, establish a strong forward network of client states in the Balkans, gain control over the Dardenelles and Istanbul, and take large parts of Eastern Anatolia. In cooperation with Japan, it may achieve an effective partition of Northern China.
... And then what? Russia still has distant and problematic naval geography for striking Britain, the French as a major military power on their western border, the Italians who will vie for influence in the Balkans, the combined naval strength of Britain, France, and Italy to oppose any real Mediterranean presence, massive and extremely difficult mountains and deserts to cross to strike Middle Eastern and Indian targets, and the vast, unabsorbable, population of China as well as Japan hemming it in in the East. Russia still has powerful great powers or terrible geography on every border, and its actual ability to pose a legitimate threat to Britain is nil up until the rise of atomic bombers and jet powered aircraft, and really has to wait for missiles to become truly effective.
By contrast, Germany's victory, in a maximalist program would gain massive colonial concessions across Africa, potentially Asia, the Pacific, move France into a firmly subjugated and almost client state stance, establish the Ottoman Empire and Austria-Hungary as southern prolongments of German power, drive German expansion far to the East and knock out the Russians as a rival power - in essence, obliterate any real military rival to Germany on land, with nobody to hedge them in. The Germans would have a world wide network of power, no remaining great power rivals, and would be free to establish hegemony over Europe and the British would be isolated and dangerously exposed. Arguably even assuming the Russian Empire achieves remarkable progress in the sciences and technology, the more technologically advanced nature of Germany and its massively superior scientific base means that up until the 1960s it would still present a far greater military threat - it is only then that I could forsee an alternative Russian Empire, as compared to an alternative German Empire, being able to develop a comparatively greater nuclear arsenal and the airpower (also another thing which the Germans are far better placed to deploy against British) and rocket power to deploy it.
Sure Russia's
absolute power in the long run is far more given its much larger population and resources, but in the short term - the better part of half a century probably - Germany is the far greater threat after victory, and perhaps always will be, given that Britain can always find allies to do the lion share of the defense against Russia, while it would have to shoulder the burden itself against Germany.
The British actually decided that Russia was more dangerous even before WWI. Their siding with Russia against Germany was partially the result of the general staff deciding that they could not protect India from the Russian army. Siding against Germany wasn't deciding it was the greater threat, it was an act of appeasement towards Russia.
Regardless, a Tsarist Russia that reached its full potential would have been more of a threat to the British Empire than Germany ever could have been. It would have been in an ideal position to strike India and the Middle East, and with Ukraine Britain could not have simply starved it out.
Which while interesting in regards to determining the British historical thinking that led to their alliance with Russia, is more useful in terms of the dangerous lunacy and unreality that has a tendency to sneak into British military thought than a realistic estimation of the actual threat potential of Russia to British India. The British general staff looking at thousands of kilometers of massive deserts, mountains which are easily fortifiable and with only a few viable passes, hostile tribes and people along the way who have clearly demonstrated their resistance to subjugation and their effectiveness against sustained occupation, almost complete lack of roads and an utter dearth of railroads, an opponent nation with major threats on both the Western and Eastern borders, and their prime colonial territory with hundreds of millions of people in it on the other side - and deciding that this was a
credible threat speaks far more to the constant British overestimation of the power projection potential of Russia in Central Asia and their own tendency to fall for their own propaganda vis-à-vis the "Great Game" than any real Russian potential to invade India.
