I know you are getting a lot of input, mine included, though the solution will be simple when you find it. It’s not going to be rocket science it will be simple and logical compared to some of the proposed causes.
That said I can tell you what it won’t be: It won’t be anything to do with the sway bar because the sway bar does not and cannot affect alignment. You can test this by removing the sway bar link from 1 or both sides and evaluate.
It won’t be any particular tire size though it could be a single bad tire no matter what size that is. You can test this by switching the rear tires side to side and evaluate. Even the tires are directional it’s OK, you’re just doing this short term.

The issue will be something that affects the steering (toe in/toe out) of 1 or both rear wheels. You describe this as occurring under moderate throttle, does it act the same under heavy throttle?