Can AI determine software engineer pay each week based on performance?

No. A software engineer’s impact cannot reasonably be measured over 7 days. It would need to be much longer, at least a month (likely much longer than a month) for junior to senior level, and even longer for staff+ level.

It may be possible to crunch enough data to determine what short term behaviors are most likely to result in short, medium, and long term gain, and then you could, in theory, peg someone’s weekly “progress”. But today I think that’s (dystopian) science fiction

It would be wonderful my competitors to adopt this method.

Piece-work programming, as managed by an "AI", is downright Dickensian.

Can you make some "AI" to do this? Probably. Would it actually measure something real and useful? Probably not. What objective measure of programmer productivity can you define and measure?

Employees would quickly learn to game such a system, or quit. It also seems like it would run afoul of employment law, because a job offer constitutes a contract even if verbal, and you can't just vary pay unless both parties agreed to that from the outset.

Sweatshop factories pay like that -- a few pennies for each label sewn in or each shoe glues together. Good luck getting programmers to work in such conditions.

Goodhart's law will really bite the company in the butt if they did this