I've always toyed with the idea of Russia winning the Great War in my head (only thing that gets me is how to get to this point without drastically changing WWI as we know it.) And while I have my regards as to why those borders probably wouldn't happen (especially with regards to a quicker WWI) I will suspend my disbelief here.
He's certainly an eligible candidate for Petrograd's purposes as well here. The wikipedia entries for Kaiser Wilhelm's children are so depressing, one committed suicide before age 30 and the others appear to have either been apolitical or involved in fascist politics. No wonder Germany became a republic OTL, this dynasty utterly failed to look out for its subjects' best interests or leave a worthwhile legacy for their kingdom.
The Habsburgs weren't perfect but they did a much better job, Charles I' peace feelers and Otto von Habsburg's role in European integration will be remembered more positively than anything the Hohenzollerns did.
Also, why is almost every Hohenzollern named Wilhelm? It's almost as confusing as the Danish monarchs' decision to name every one their son Christian or Frederick.
You got me, traditionally, Hohenzollern monarchs (at least from the formation of the Kingdom of Prussia to the fall of the German Empire) were traditionally named Frederick (Friedrich), William (Wilhelm) or Frederick William (Friedrich Wilhelm). While this has largely changed after the death of the Crown Prince (mostly because the actual next in line predeceased him) that's generally the rule of thumb. The Danish decision I think was only because it just became tradition.
But if Russia were to establish a German client state (which East Prussia, or rather what it would probably be called, the Duchy of Prussia, or Grand Duchy of Prussia, Royal Prussia was largely defined as West Prussia, which in this scenario is under direct Russian control) I can see August Wilhelm taking up that throne, even though it would make him the Louis Philippe to the German Hohenzollern Legitimists, assuming the Hohenzollerns manage to keep their throne.
Will Russia end up promoting monarchism around the world instead of communism? It would be an interesting reversal to see Russia backing the Arab monarchies instead of siding with republican Arab nationalists OTL.
Without fascism and communism, the world could have way more monarchies around in the 21st century. Serbia, Montenegro, Greece, Bulgaria, and Romania might all remain monarchies ITTL. This is the current Romanov heir btw, Grand Duchess Maria Vladimirovna.
With Russia still around, I can see monarchism still being a fairly prominent political force. Even though its unlikely that it will be the style of absolute monarchism of old, more like the Kaiserreich-styled Authoritarian Democracy at best. I wouldn't count out fascism though, if only because the ideology is still there with Mussolini and he could still rise to power ITTL, even if it won't in Germany (since the prominent reason for it rising in Germany, a large and powerful communist state close to the border is replaced with a monarchist one.)
But with communism not gaining prominence due to no Soviet Union (assuming Germany doesn't fall to communist revolution first) then yeah, I can see the countries that made it out of WWI as monarchies remaining as such (except maybe Greece, but that's a story for another day.)
By the by, Maria Vladimirovna is the current heir (or rather the most widely supported current heir) in OTL, ITTL, it's not exactly as clear cut, and with no Russian Revolution, you can make the argument for many other potential claimants.