So let's say the February revolution still happens just like OTL and the Czar is overthrown and replaced with a provisional, democratically elected left-wing government
You do realize that if by "provisional, democratically elected government," never mind if it is left wing or not, you have a flat contradiction to "just like OTL," don't you? I don't know whether to hope you do or don't know this is not what happened at all.
The February Revolution was not, like the October Revolution, a coup carried out by an organized revolutionary cadre with central command and a set agenda. It was triggered by a bunch of women who had simply had it with the latest ration cuts. Certainly the ability of the unorganized mass rising in Petrograd, soon followed by other such in other centers in Russia, to neutralize all Tsarist authority and maintain a form of order had a lot to do with general propagandizing of the masses by various rival groups, including the Bolsheviks. It also took a lot of self-organization from the dress rehearsal as it were of 1905, when the first Soviets emerged, which in turn were a synthesis of various left-wing programs and grass roots straightforward pragmatism. "Soviet" means "council" in Russian. In '05, various groups rising up seized control via organizing citizen councils at the grassroots levels, and these bodies claimed the authority, via direct democratic deliberation, to make the rules and set the policies; the Bolsheviks retroactively praised them; don't know what other radical groups such as the Social Revolutionaries, non-Marxists with their major support in the radical left wing out in the villages as radical agrarian populists, and in their right wing among various bourgeois intelligentsia. Alexander Kerensky was I believe a lawyer for the SRs and probably correctly described as a Right SR.
So in February 1917 (March on the Gregorian calendar, as the October Revolution was in November on those western calendars) the power that emerged was dual. The soviets reformed and had substantial power, such that the "Provisional Government's" orders were followed in Petrograd and most other places only with the city Soviet's countersignature. If you ask me, the Soviets were the proper and only government of Russia in these days.
The so-called and self named Provisional Government on the other hand had zero claim to
democratic legitimacy. It was and throughout its existence remained a committee of self-appointed notables who simply pretended to inherent the authority of the Tsar--as noted, this was taken with huge grains of salt even by the more conservative of the residents of Petrograd and other key cities who comprised the makeup of the numerous grassroots soviets, each of which elected delegates to the city Soviet mentioned. It mainly impressed foreign governments, notably the Entente allies soon to include the USA. It was in their interest to pretend that the PG was in fact some kind of legitimate thing, and their influence that provided much of the PGs leverage in Russia.
As a pragmatic move, in view of the plainly leftist populism tending to dominate the Soviets, the PG prudently named Kerensky, as left wing a figure as they could find among themselves, to be the nominal head of their little clique. Had they been as forthrightly reactionary as their membership would suggest, they would have had to fight the Soviets head on, and given the sympathy for the Soviets by the larger part of the Army at this point (the Army was mostly recruited from the peasant majority, but over the years of painful war, lots of leftists punitively drafted to remove them from being able to agitate in the motherland grassroots agitated among the soldiers instead, and their constant getting kicked in the teeth by the German forces combined with revolution in Petrograd made the armies pretty much revolutionary too) I would not bet on the PG and its sympathizers lasting a day. In fact, the PG seriously considered trying to get the monarchy restored, either via instating some other high ranking Romanov or perhaps starting a new dynasty--even they recognized from the get go that reinstating Nicholas II himself was clean out.
If you take the position that the PG was in some sense a legitimate government of Russia, you have to also conclude Russia had no democracy at any point. By the time of the October Revolution, the PG had called a Constituent Assembly to draft a constitution for Russia, but it was in the middle of deliberations when the Bolsheviks shut it down. Nor do I think it was a particularly representative body itself, certainly its delegates had not been chosen by democratic means!
I consider the Soviets to have been the real and democratic government of Russia, but it is a sad fact they did not quite have the self-confidence nor generally granted authority to just shut down the PG's pretensions and take the reins as they were.
What you did in your OP, striking the "just as OTL" bit, was call for a POD right during or before the February Revolution, in which the people of Petrograd and other rising cities, in the middle of fighting off the authoritarian power that had ruled them all their lives and history before, with a brief interim in 1905 subsequently tricked into surrendering power and shunted aside, took some time for the side issue of organizing agreements to some sort of consensus democracy however ramshackle. To a degree that happened--the Soviets formed, and their authority was accepted by revolutionaries and most people.
The straightforward way to change the February situation to come close to your OP, barring the "just as OTL" bit, would be if several factions cohering in the city and grassroots Soviet leaderships had judged the PG's pretensions to be dangerous and agreed to take action immediately to disperse them, and explicitly repudiated their claims and assumed the mantle that the PG pretended to. I am hazy on certain aspects of the events of February but I believe there were weighty reasons no such consensus emerged and the PG was left standing to make its insidious claims of authority.
A variation on the theme would be if the factions favoring abolishing the PG agreed with more cautious or conservative ones at the time to compromise in a resolution for the Soviet to insist on demanding the PG be reviewed and purged of unacceptably reactionary elements by the Soviet, and operate as an "upper house" to the Soviet thenceforward, with agreements of the "higher" aristocratic-bourgeois body to be bound to coordination with the populist Soviet. But I honestly think that would just be circling Robin Hood's barn; sooner or later the Soviet would become fed up with its reactionary agenda and just shut it down. Perhaps in doing so it would unleash another round of civil war as the aristocratic and bourgeois circles--a tiny numerical minority, but commanding great wealth and considerable pre-revolutionary institutional experience, albeit with feckless outcomes!--drew around them a bodyguard of the more conservative popular elements who would thus be in rebellion against the Soviets, which would presumably become more leftist and radical as a result of this voting with their feet of the right wing elements. In this knock down fight, with the Germans still pressing at the heels of the Russian army on the fronts, I am not sure what the outcome would be but I would bet on the Soviets.
In turn, while in Russia as a whole, the SRs as party of the countryside would command a lot of scattered support, the Bolsheviks tended to gain more and more influence in the city soviets, and so this trajectory amounts I think to moving the dates around in the OTL 1917 process, if anything accelerating the day the Bolsheviks, perhaps still with left SR allies, take control of Petrograd and other strongholds in Russia, leading to the long OTL Civil War, in the course of which the left SRs probably still would break and be driven out of power and out of Russia ultimately.
What you need is to establish in Petrograd and at least some other Russian stronghold cities, and in sympathy with it among the troops, some ATL third party, or change the role of the SRs to take this role, so as to check the rise of influence of the Bolsheviks in the city soviets. Perhaps, if he observes that the Bolsheviks cannot gain complete control of the city Soviets and that a violent uprising by Bolsheviks alone would be overcome and destroyed, Lenin might shift, grudgingly, over to parliamentarian tactics and forge a lasting alliance based on a balance of power with selected other Russian left wing movements, and the multiparty dynamics resulting would sustain Russian democracy, presumably still centered in and based on the Soviet system, through an ATL October that sweeps aside the PG and its adherents but is stuck with meaningful democratic accountability via multi-party competition in the Soviets.
