East Germany for the purpose of the OP scenario effectively means 'Prussia'. Calling it East Germany is a big misnomer that only confused the issue.
Of course, you cannot force any major split without actually marching troops into Germany and enforcing it. Occupation. That was not something the Entente wanted to do. So the scenario is kind of doomed from the beginning. It would not have been possible without some major changes in how UK, USA and France thought.
Problem: Austria was not on the winning side of the war. If the allies decided to annex Old Bavaria, they would have given it to Switzerland or to Czechoslovakia, but not to another looser of the war.
Both of those options are complete non-starters.

Bavaria is not just some no-name province but the third most powerful German state after Prussia and Austria. You would not turn Bavaria Swiss or Czechian, you'd turn Czechia or Switzerland Bavarian. Especially since both already have large German populations, making any remaining languages the clear minority in the resulting hypothetical nation.
The natural division would be dissolving Germany and returning to Prussia, Austria & friends - Prussia leading something based on the North German Federation. With the south maybe united into a counterweight South German Federation of Bavaria, Württemberg and Baden. Maybe add Austria too, but that is not a natural construct and could threaten to fall apart again. And you still would have to invest a lot of effort to keep the two (or three) nations apart permanently. Occupation is only the beginning, you'd need some long-term plan how you can drive a large enough wedge between them to prevent unification desires. While in OTL communist and capitalist ideologies were ultimately not strong enough for that, a north/south divide would be more along actual cultural lines and anything based on that may have a better chance.
There's also French dream of propping up an independent Rheinland based on Rhenish nationalism (here that would mean splitting the majority Catholic West German territories of the NGF away from Protestant Prussian dominance). But that never worked out as a viable entity in history, even though it had some institutional/traditional traction. It would probably collapse since it would be seen as a French puppet - which would of course be true.