Potential PoD might be that in 1916 the Central Powers manage to completely take over Romania, stripping it from all useful resources and disarming it, thereby creating a more weakened and unstable situation by 1918.
It already did so IOTL, how you can make the situation worse than the entire country starving and Bucharest being "without bread" in 1919?
As early as summer 1918, German authorities were noting the social and political implications of an expanding famine in Romania. Heavy usage and requisitions had produced shortages of draught animals, manpower, machinery, and tools, resulting in rapidly falling agricultural production. Romania's staple industry was in chaos after almost two years of effective Raubwirtschaft. German sources, for example, reported in January 1919 that wheat flour had disappeared entirely and that "the city of Bucharest is without bread". Romania ceased to export grain at all, instead importing grain and other foodstuffs as grain production fell to thirty-five percent of prewar averages in 1919 and 1920. Indeed, Romania was reduced to pleading with Herbert Hoover for emergency assistance in food, clothing, and shoes. Soon thereafter the Romanian state was forced onto the international grain market, exchanging its treasury notes for foreign grain, reselling the grain domestically at a steep discount." Domestic production had plummeted and domestic purchasing power was deeply reduced, such that Romania could neither feed itself nor could its inhabitants buy food with the cash on hand. Instead, food had to be purchased against future income.
Page 20-1 (470-1).
The rest of the war goes mostly as OTL, with the exception that Hungary manages to retain a government that is an acceptable partner for the Entente (perhaps the Karolyi government does not happen and a lot of turmoil is averted).
Karolyi was as Entente friendly as one could get, he did EVERYTHING they told him to do. Problem was the Entente is much more concerned with giving its allies territories than respecting their principle of self-determination for a CP member, not the leader in charge.
However, as the occupiers leave, Romania remains plundered and unrest leads to the Communists seizing power, probably with Russian help.
Only way I see the communists taking power is the Bolsheviks marching all the way to Bucharest; the Romanian Communist Party was formed by radical members of the Social-Democratic party in
1921 which is WAY too late for any communist uprising.
Would the Entente intervene?
Just supporting the "White" faction would be enough for any "domestic" communist uprising, but if need be the "Armée d'Orient" is still in the area IIRC, and what went to Odessa IOTL would be redirected to Romania; in case of a Bolshevik invasion and Romania is overrun they would be a little bit more careful, though they would likely intervene to restore the Kingdom.
Could Poland (probably not) or Czechoslovakia?
Poland has an ongoing war with the Soviets and likely no land connection to Romania- they have other priorities, Czechoslovakia still has Hungary in the middle as Carpatho-Ukraine was still under Hungarian control ATP.
Could the Russians provide support?
It's unlikely they do much, they didn't support Hungary IOTL; so any domestic communist uprising will likely be left on its own soon to be crushed by the "Whites" and ends up being what the HSR is today
at best- a footnote and an interesting POD. A Bolshevik invasion, interesting it may be, is not very likely either, they have MUCH more important priorities during this entire time; at most some minor border changes in favor of the (future) USSR.
If Romania remains firmly Communist and allied with the Soviets they would probably not get a seat and the table and the Entente might go easier on Hungary as they want to avoid the Red spreading further?
They wouldn't give any more territories to Romania (though seeing the state of the Hungarian army, the communists likely take a lot of land from them; and a good part of former Hungarian territory was under occupation from very early on regardless of further border changes) and since the Hungarians and Bulgarians aren't as hated by the Big Four as other belligerents are, they likely are allowed to have a larger army than OTL (though still with restrictions).
Assuming it survives the Interwar period and events in Europe are roughly the same (Great Depression, Hitler takes power, war starts over Poland...) the fact that the Germans would have to invade Romania and lack its resources at the beginning mean more casualties and their advances in the USSR are stopped sooner; though they do benefit from the fact that Hungary has a larger army (but still claims on Czechoslovakia and Yugoslavia which ensures it to come in their sphere). Bulgaria might not join the Axis until much later since IOTL it was essentially bullied into doing so by the Germans, who now have much more difficulties in doing so. Romania would be expanded at the expense of Hungary and Bulgaria post-WW2.
Hard to see a scenario where this doesn’t end with Hungarian troops in Bucharest (for a second time) to be honest.
Why would there be Hungarian troops in Bucharest? Also what Hungarian troops, the few divisions that have not been demobilized?
However, if it does succeed I could foresee the authoritarian movements in the Balkans
What kind of authoritarian movements in the Balkans?
I’d expect the Allies to go easier on Austria and Hungary, maybe even allowing them to keep large armies.
Austria is completely disconnected from Romania, why would they be allowed to have a larger army?
I think Soviet-Romanian linkage is possible and if so the question becomes - would Romania be annexed as an SSR?
If we assume a domestic uprising then probably not, and there would be little benefit from annexing it later on, though in practice the difference would be minimal as any Soviet leader could do as he pleases.