The Internet Archive still thinks it has a legitimate fair-use, first-sale, & library rights basis for 1:1 controlled lending of ebooks for which physical copies are held.
With the advice of competent counsel, IA clearly estimates its chance of prevailing on that question as worth the continuing costs.
At worst, they lose on that question, and then comply with the August 2023 settlement & pay some undisclosed amount to publishers to cover publishers' legal fees.
At best, they set an important precedent that saves their (and many others libraries!) ability to lend in the digital era for the one-time cost of a physical book, instead of the new time-limited leasing models publishers are imposing for native ebook lending – which could massively increase library costs even though digital delivery could be far cheaper than physical lnding.
Note that even if the odds are long, setting that precedent would be very valuable! The calculation isn't, "are we more than 51% likely to win?", but "even if we've only got a 5% chance of winning, is the win valuable enough to spend for the chance?".
What if Sony had given up when the 'Betamax' case was going against it? It appealed to the Supreme Court, and won a unambiguous ruling that home recording of TV was legitimate fair use.
That's a result the rightsholders, and those who naively adopt rightsholder-like copyright-maximalist reasoning without acknowledging the counterbalancing factors in the law, had alleged was preposterous. "Clearly illegal!" they said. But despite that bluster, the actual highest court decided otherwise.
Without that ruling, VCRs and DVRs would have arrived far slower & on a short-leash fully controlled by incumbent big studios.
Why bother appealing then? Seems to just be wasting lawyers fees on both sides.