Earlier quoted context omitted.
Code correctness should be checked automatically with the CI and testsuite. New tests should be added. This is exactly what makes sure these stupid errors don't bother the reviewer. Same for the code formatting and documentation.
What exactly is the analogy you’re suggesting, using LLMs to verify the citations?
One could submit their bibtex files and expect bibtex citations to be verifiable using a low level checker.
Worst case scenario if your bibtex citation was a variant of one in the checker database you'd be asked to correct it to match the canonical version.
However, as others here have stated, hallucinated "citations" are actually the lesser problem. Citing irrelevant papers based on a fly-by reference is a much harder problem; this was present even before LLMs, but this has now become far worse with LLMs.