seems i can't edit my post
forgot to mention: it has to work at 5V, and if the eeprom size is different, check that the page size is 32 bytes, since a firmware written (properly) for the original eeprom (as per the BOM) would expect the page size to be 32 bytes
if you're gonna use FRAM - the page size won't matter
the eeprom you linked is 8KBytes, automotive grade, the pinout matches, it's SOIC-8 (you'll need an adapter), it has some extra fancy features, i guess it shouldn't be a problem, the page size is 32
this one should certainly work:
https://eu.mouser.com/ProductDetail/Mic ... %252BOw%3Dalso 25LC320A-I/P (same as above but different operating voltage range, still runs at 5V)