I am getting a message in my mail app saying: Connections to the server “p45-imap.mail.me.com” on the default ports timed out.

Check Apple System Status - iCloud mail is experiencing issues affect some customers is 09:30 PDT Today May 27, 2021 and is ongoing.

Apple - Support - System Status

I got a similar message.

It was a transient network or server issue that has resolved itself for me after a while.