I ran into the same thing today. I tried to send an email and it said the outgoing server wasn't working or something like that.
I went to Mail > Preferences > Accounts. Under the Account Information tab, I clicked on the Outgoing Mail Server (SMTP) dropdown and chose Edit SMTP Server List. Under the Advanced tab, I reentered my password. (Since I have 2 step verification enabled, this was the app password that I had previously generated.) After that, Gmail didn't show as being offline and the email went through.