Yes, when your smtp server communicate whit others it needs to be trusted (ensure own crypto capabilities and authenticity). For this smtp use own certificate. This certificate should be subjected to your server hostname. You can inspect what certificate smtp use by this command.
echo | openssl s_client -connect name.mailserver.com:465 -servername name.mailserver.com 2>/dev/null
What mail is send came after establishing this link and in terms of certificate for smtp server does not matter if it’s user@dom1.com or user@dom2.com, on this level you are using DKIM, SPF, DMARK to be trusted.
Just quick note. If you are using own LE solution be sure you are always loading current certificate. Not sure how Mailcow but other servers caching certificate on startup and does not tracking source change. There is possibility you will need to restart smtp server to load renewed cert. To test expiration of currently used cert you can use this command (This should apply to dovecot as well,… for imap,…).
``````echo | openssl s_client -connect name.mailserver.com:465 -servername name.mailserver.com 2>/dev/null | openssl x509 -noout -dates```