For Gmail to continue working with Apple Mail as it does now, I suppose you mean. I'm not worried about the former continuing to work, but the latter with POP.
I was thinking of asking if I should do that now rather than later, but that seemed suspiciously like an overly stupid question and so I'll try it now in accordance with the link provided.
{...]
I don't see the App Passwords option, presumably because I don't have 2-Step Verification turned on. There was some reason I didn't want 2-Step Verification previously, and I suspect I have the same reason now – a non-US phone number, maybe. But I'll give it a try.
[...]
Okay, it's on with text messages to my non-US phone, but I immediately got the dreaded "Mail Password Required Enter your password for "[...]" in Internet Accounts" alert, which always hangs me up because then it says... yup, "Unable to verify account name or password."
"Login Failed" – ****. This usually goes on for hours or days. I have a file with collected instructions on what to do about this, but it's never clear what if anything causes it to stop. One of the tips is to sign out of Google, but if that ever works it's not working now. I can try quitting and rebooting Mail... nope. Shutting down and restarting the Mac... nope. Likely because I turned on 2-Step Verification, I suspect, and Apple Mail can't get through it.
I turned off 2-Step Verification and Apple Mail immediately worked again. It therefore unfortunately appears that App Passwords can't save me, as I have to have 2-Step Verification on to have the option and if I turn it on Apple Mail doesn't work.
There's one more thing I can think of to try in regard to App Passwords, and that's turning 2-Step Verification back on, creating an App Password, and then turning 2-Step Verification back off, hoping the App Password will still be retained. I doubt this will work but I can try it.
[...]
Whoa! Now it worked, and without turning 2-Step Verification off. Let's hope it keeps working after May 30. Thanks!