Use the google service, instead of trying to reinvent the wheel https://support.google.com/accounts/answer/3024190?hl=en

Archiving in Thunderbird simply places mail into the all mail folder on google.

The Google Takeout service backs up Gmail by putting it all into one zipped MBOX file. Third-party software is required to open and view it. That's not what I want. I want a bunch of .eml files that are easy to access when I am offline, in a folder structure that replicates, as nearly as possible, the nested tags in my gmail account. The instructions at [https://support.mozilla.org/en-US/kb/archived-messages] show how to accomplish this, but they don't explain whether the messages are moved from the server into the local archive, or copied. I am not sure what you mean by messages being placed into a folder on Google. If you meant that the messages are stripped of their tags so that they only show up under "All mail", that seems to be what happens if one hasn't yet configured Thunderbird archiving under account settings. What I want to know is what happens to the messages on the server after Thunderbird account settings are configured to store archived messages locally. Do the messages get snatched away from Gmail, or are they copied, leaving originals still on the server?

Sally-Mae said

The Google Takeout service backs up Gmail by putting it all into one zipped MBOX file.

I though this sounds wrong, so I just used the takeout service. It took this long to build the archive.

What i got was one mbox file for each folder. So I got an archive.mbox, an inbox.mbox etc.in my case 6 files in all. So it does not put it all into one zipped archive.

Third-party software is required to open and view it.

Thunderbird is that third part software.

That's not what I want. I want a bunch of .eml files that are easy to access when I am offline, in a folder structure that replicates, as nearly as possible, the nested tags in my gmail account.

Not going to happen, Thunderbird does not store mail in EML files. it uses mbox files. The same sort of files gmail provides.

but they don't explain whether the messages are moved from the server into the local archive, or copied.

The default is the archive folder for gmail accounts is the all mail folder. You can override that location, but it is a bad idea to move from the server to local storage more than a few hundred messages at a time. You are looking for a full archive, so it is going to talk you a lot of time archiving them one at a time, moving them from the gmail server to local folders.

I am not sure what you mean by messages being placed into a folder on Google.

IMAP mail accounts are synchronized to the mail server any action you take in Thunderbird is replicated on the mail server. Including moving or archiving mail outside of the mail account to say local folders. This is interpreted as deletion from the mail server.

If you meant that the messages are stripped of their tags so that they only show up under "All mail", that seems to be what happens if one hasn't yet configured Thunderbird archiving under account settings.

Correct

What I want to know is what happens to the messages on the server after Thunderbird account settings are configured to store archived messages locally.

They are deleted.