I’m using infomaniak. Bought my domain via them and got a free mailbox with it + simple site hosting (kualdir.eu for example).
Just looked myself up on whois and no info about me can be found as of yet.
The only “issue” you may encounter is while moving mail provider you may need to take a more expensive option than the non-custom domain ones. At least, that I know of ofc.
I’d love if there was a way to hook this onto apps like discord to automatically compress images too big to upload