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Yes, quite straightforwardly. Works may be copyrighted, but all the ideas and stylistic choices which comprise that work generally may not.

That the implications of this idea have the “wrong” winners and losers is a separate matter.

Copyright protects mainly against the distribution of works, not about consumption. It is not the access to the library the bit that is illegal here, it is illegal for that library to distribute works without the copyright holders permission. You might like it or not (I don't), but copyright laws are fairly straightforward.

Regulators were convinced LLM/AI will increase GDP by infinity, while you getting a single book for free creates a hole in VAT budget of 2$.