You can get by for most apps with MicroG which is a cut down implementation of play services but some apps will absolutely refuse to run on a non-factory Android image.

Last time I was on a custom ROM I got most things to work to some extent but some jush didn’t work e.g. NFC payments via Google Pay.

IIRC there’s legislation being discussed in the EU that could compel Google to offer hardware signatures for custom ROMs in future.