Of course they can just opt out of participating. But I guess if they have to process opting out of thousands of claims that will be an annoyance.

Are you going to file with the Copyright Claims Board...?

Correct; but that's not the issue here. Anthropic was absolved on training as a fair use. The matter heading to trial was plain old copyright infringement, and active publishers are exclusive licensees (whose rights are infringed alongside the author).

For in print works with large publishers, there is usually a defined process for the defense of any infringement and recovery/sharing of proceeds. Very generally, we believe the standard is the publisher can deduct its costs (here de minimis to nil) and then any award is likely split w/ the author.

There will be an official database that everyone can check, and it will be different from what has been available so far online. Unless the judge imposes something as part of the settlement, most splits would be determined by your publishing contract(s).