I would do any and all of this forwarding at the server. It's not efficient to do it in a mail client. And the mail client has to be up and running to be able to process messages, so it's not very useful if you're away from home using your mobile device, and your only instance of Thunderbird is on the switched-off machine at home.

Is the gmail account installed in Thunderbird? Is it possibly return forwarding back to the verizon account?

Gmail do a few silent things, such as not honouring Cc: to self; they reason that you'll have a copy in Sent aka All Mail, so you don't need to send yourself a copy. I don't know if forwarding has any similar strictures applied to it.

In the future, as Zenos recommends, I will not ask a mail client to do automatic forwarding. I apparently did do this, though, telling Thunderbird to forward emails to Gmail, and now all emails sent to the verizon.net account, to which Thunderbird is linked, show up only in Gmail, not in Thunderbird. How do I undo this?

No, the Gmail account is not installed in Thunderbird. I understand that there's some way to do this, and perhaps that would be a workaround that would help me, but I'd rather go back to where I was three days ago with emails sent to the verizon.net address appearing in Thunderbird without Gmail intervention.

I need the Gmail account because some sources, notably the service that produces online bills with my city's water and sewer charges, refuse to recognize my verizon.net address as valid. So I have them sending the bills to the Gmail address and Gmail has, quite reliably, been forwarding them to the verizon.net address where I can see them in Thunderbird. Only until now, however! Now no new emails appear in the Thunderbird inbox. If sent to the Verizon address, they show up in the Gmail account and only there.

I think you need to add that Gmail account to Thunderbird.

Go to File|New|Existing Mail Account and fill in your gmail credentials. With IMAP and SMTP, the default authorisation method will be OAuth2 which makes it about as easy as is possible. You'll be shown a webpage (in Thunderbird) that asks you to log in to your gmail account to confirm you are the legitimate user of that account.

POP is a bit more fiddly. It doesn't support OAuth 2 and you may be obliged to either set it to trust "less secure applications" or use an "application-specific password".

https://support.google.com/accounts/answer/185833?hl=en

OK, I've set the account up with POP3, specifying access for less secure apps. I don't know what OAuth 2 is, but I don't think I need to know.

Still nothing comes into the verizon.net Inbox, just into the Gmail one. I could wish that unused folders like this could be hidden so that they don't clutter up the folder pane. (The Drafts folder in Local Folders is another useless bit of clutter.) It doesn't seem to be possible to delete them.

I use Box Sync to back up my Thunderbird folder and have put together instructions to restore it on the inevitable day when my computer dies. Since all messages are still contained in the folder, there is no need to change this.