Has such a scenario been done in a TL before, and if so, where?
I'm working on it. Granted, it is (a) an ASB timeline where the ASBs are mecha, (b) a Central Powers victory timeline, and (c) I haven't gotten into detail with Russia because the focus of the story is in the eastern Mediterranean. But the gist of it is that the White Movement manage to cobble itself together into a loose federation after quashing the Reds and getting stuck in an endless stalemate in the ensuing infighting that leaders felt shouldn't continue, lest the foreign powers continue to prey on them.
What would the ideology of the central Russian government likely be? Would it be a restored monarchy? Some powerful White general like Wrangel, Denikin or Kolchak calling the shots? Or maybe a democratic republic, like the one established by the Constituent Assembly of 1918?
Likely either a conservative stronghold or a revolutionary republic, but the details concerning it can be anything under the sun. Monarchy thou... that depends. Tsar Nicholas II isn't going to get it back, even if he survives his OTL assassination. His brother refuses to take it up. So that leaves the squalling mess of branch families around them. Not impossible, but it depends on who gets the crown, and who's in power to give - or not give - the crown.
What would the warlords and warlord regions be? The White movement had a plethora of colorful personalities. Wrangel, Denikin, Kolchak, Yudenich, Kornilov, Diterikhs, von Ungern-Sternberg... Anyone else?
A few ideas would be the Caucasus under the Cossack republics, Crimea, maybe a smattering of warlords in Siberia. Ungern-Sternberg Mongolia is a popular one, but it's hard to see him stay on with his hackneyed style of rule, unless you are me and decided to do it anyway because it's the Mad Baron.
Would there be a Communist holdout, like in China? Not necessarily Bolshevik - the Komuch or Georgian Mensheviks could realistically fill that gap, imo. If so, where would its center of operations be and would they still have a chance to return to power? And if the far-left forces in Russia are pushed to the countryside and are forced to establish their base within the peasantry rather than the city proletariat, could something like a Russian equivalent of Maoism arise?
Very likely, but the problem is, where would they hide? The Chinese communists had the benefit of bad terrain, sympathetic locals and horrendous incompetence in their pursuers to escape in the Long March. Russia? You'll either freeze to death in the empty wastes of Siberia, get hunted down in the forests of European Russia or hide in the hideously hostile society and terrain of Central Asia. Exile is an option though.
How long would the Russian warlord era last? I couldn't imagine Russia staying divided for long - so if there is an equivalent of the Nanjing Decade, who would lead the charge for Russian reunification?
Depends who has the will, and who has control of European Russia, with all its manpower and resources. Historically, that would be the Bolsheviks, but in the case of a White victory, it depends on who has the bulk of the territory in that region.
What impact would the lack of a united Russia have on the Interwar period? The Nazis probably won't rise to power without the Soviet threat and communism would have its wings clipped in general... What about the impact on Eastern Europe, the actions of the Entente victors, USA?
Loads. Maybe an extension of the Warlords era from China? Forays into China by Russian warlords and vice versa. Poland, Finalnd and Ukraine trying to carve out its place in the sun. Western powers jostling for influence with the Japanese. Practically anything can be possible with enough thought into it.