Assume a binary of two solar-mass stars. How far apart could they be before they would drift apart?
If they were intergalactic stars, quite far away. The drift-apart distance is determined by other objects in the area that might steal one of the partners, rather than any intrinsic limit.
In galaxy, I suppose this would mean that they would have to be significantly closer to each other than any other comparable stellar-size object. Proxima Centauri is about a quarter light-year from its partner stars which seems to be a good heuristic limit.
Isn’t there some doubt as to whether Proxima is actually part of that system or just a star that happens to be nearby?
Yes there is. But if a quarter light-year was really too large, the ambiguity would already be resolved. 