I'm not sure if you're actually gaining war exhaustion because of a bug, or at least, I'm not, but it might look like it because of how it works. (Or it could just be a bug I've not seen!)
You loose war exhaustion based on what you loose in the battle, and if you're not using the beta patch it tries to tally up who lost what and figure out if the battle was "won" or "lost" based on that. If you take a planet but loose a dozen armies doing so (quite a possible outcome since Defensive armies are super stronk right now) it'll show up as a loosing battle because you got a ton of war exhaustion from the loosing armies whereas they don't get exhaustion from the loss of their defensive armies (although they do get some from loosing the planet, I'm not sure if that counts for the battle calculations, I suspect not, and even so it's possible to take a planet and get more exhaustion then they do from the planet loss). Similarly if you fight a beefed up defensive station you can loose ships to it, which give you war exhaustion, but then it'll not give the enemy any, and so it'll calculate the battle as a loss.
Now, if that's the issue you've been facing, it's not really a bug so much as an unclear UI, they've "fixed" it in the beta patch by making it so the battle tracker no longer tries to figure out what was a win and what was a loss, but just tells you who got what war exhaustion.
Anyway, the beta patch makes it easier to subjugate people apparently (haven't tried it yet so idk.) and also makes it so that wars don't autoend at 100%, instead you get big penalties but can keep going. So you can have those big war goals it should be more possible. Otherwise I found it possible to persecute big wars successfully by really crushing my opponents so hard that I took no war exhaustion from fights. With big enough fleets and huge fuck off armies I found it possible to win most victories totally before ticking exhaustion got me. But I didn't go up against a galaxy wide federation yet, so ymmv.