Mozilla's email-related service is https://relay.firefox.com/ which obviously needs to rely on quite a bit of Mozilla infrastructure in its default incarnation, and is probably a fair bit harder to self-host than Firefox Sync.

Is Mozilla Relay (email) really needed for Sync?

Relay is unrelated to that conversation.

That is also unrelated. Firefox Sync itself requires Mozilla Accounts to function at all, which requires email for verification and password reset. To properly self-host Firefox Sync you need those parts too, which includes an SMTP server (or substitute).

The other way around. Server-side email verification for accounts and password-reset is an integrated part of the flow and also needs to be hosted and wired up, unless you want to dig into the code and patch those parts out.