Only with MTA-STS enabled for the server will an SMTP client (that's delivering to an SMTP server) verify the TLS certificate against PKI (with DANE, it's verified against "self-signed" or CA certs in DNS). (I'm the developer of a mail server that sets up TLS for SMTP with MTA-STS and DANE using Let's Encrypt certificates by default).
I have never heard of any SMTP server doing TLS client certificate authentication. I'm pretty sure there's no standard for that, so it can't be a requirement for all incoming email. It could be a requirement between parties that have made agreements about that explicitly. And theoretically, some mail servers could use it as a signal of authenticity of the sender. But email has other, standardized mechanisms for that. And I suspect you might see delivery failures if you start requesting TLS client cert authentication from all SMTP clients.