Mozilla help site directs me to find things on PC that I can't locate or understand. Not very tech-savvy, pretty frustrated.

That would indicate you need the assistance of professional folk, not free internet peers.

Lets look at this. You have downloaded your "recent email" so the connection is working.

1. You appear to think that there is something more to download from the server. What makes you think there is anything more on the AOL servers to download?
2. Have you tried logging in to their webmail portal to see if there is more there to get? I understand that Yahoo, AOL's parent have instituted some sort of limit on how old mail that is routinely downloaded can be. But I have no details.

The connection is NOT working. “Log in with password …..did not succeed”(or similar.) Recent emails downloaded only while in PAID AOL help session, once agent was no longer sharing my screen, no further download. I can receive my mail both on AOL webmail and on iPhone, using phone’s email app—couple dozen per day. Have just the one active address/account. Newly reset AOL password is only relevant one I know of.

The connection is NOT working. “Log in with password …..did not succeed”(or similar.)

The error messages are the only clue we get as to why your not connecting. So unless you can post the messages verbatim then we will be stuck in a Chinese whispers situation. I have no idea what the actual error is because you have not posted that information.

Recent emails downloaded only while in PAID AOL help session, once agent was no longer sharing my screen, no further download.

I really can not comment on what changes between a shared screen and a normal situation. It does however indicate that the problem is not Thunderbird but something else on your computer. Could it be you had to disable some software to allow them to share your screen, like your antivirus or VPN?

I can receive my mail both on AOL webmail and on iPhone, using phone’s email app—couple dozen per day. Have just the one active address/account. Newly reset AOL password is only relevant one I know of.

Then I suggest you read up on app passwords as they are, as far as I know, becoming a requirement at AOL. https://help.aol.com/articles/Create-and-manage-app-password