Congress is getting lobbied for new laws on who owns the content that AI models are being trained from
Training AI from something definitely can't change who owns that thing. This is ridiculous and I'm pretty sure isn't being considered.
If I let AI watch Frozen does that change who owns it? No Disney still does.
who has to pay who for the privledge of using that data
IIUC most of the laws talk about if AI training is "fair use". If it is fair use copyright protections don't apply. But granting a license to your work won't change that.
The only thing I could see potentially being done would be changing the default copyright protections to allowed a revocable default grant for AI training. But it isn't even clear if granting a new license would implicitly revoke that default grant. It also seems unlikely that this is the way the law would work.