I'm using Bunny DNS and it's been mostly unremarkable (which is a very good thing for a DNS provider)!
The only annoyance is that their domain import auto-detects existing records, but it seems to miss a lot of them so you end up manually copying a lot of things over anyway.
Almost no mainstream existing provider you’re migrating from would support AXFR from Bunny’s servers. But yes, AXFR would be the ideal solution in a perfect world.
iirc at least some providers let you whitelist AXFR for migrating away from them, but seems like it is usually only if you pay enough (i. e. restricted to enterprise plans).
Since it's much rarer than I thought, I guess it makes sense bunny haven't implemented support for ingesting with AXFR.
I'm a BunnyDNS user and wanted to share a warning - the import from a zone file can drop records silently, and the export will fail to export some of your records. I reported bugs some months ago, they replied they've fixed some but it's still a problem.
Spirit: ensure you keep a good copy of your zone files (bind format), their import / export has issues (it also doesn't include SOA or NS records). I spent time (before the recent fixes) manually validating records.
The only annoyance is that their domain import auto-detects existing records, but it seems to miss a lot of them so you end up manually copying a lot of things over anyway.