That makes sense. However, I am generally biased against making significant changes in software (especially rewrites) without also beefing up the test suite, though.
You can write frivolous tests all you want; bugs are a part of life. They'll occur even if you test thoroughly, especially in new software. It's the response that matters.
First - cases where expected+old+new are identical, should go to regression suite. Now a HUMAN should take a look in this order: 1. Cases where expected+old are identical, but rust is different. 2. If time allows - Cases where expected+rust are identical , but old is different.
TBH, after #1 (expected+old, vs. rust) I'd be asking the GenAI to generate more test cases in these faulty areas.
Usually, the standard a rewrite is held to is "no worse than the original," which is a very high bar.