Thunderbird work within the rather bizarre implementation of IMAP Google uses. The illogical actions you observe are a direct result of your and googles setting on the web site.

Gmail uses Labels to define folders. That is not how IMAP works, it uses real folders with real emails in them. Gmail also uses all mail to hold all of your mail. All folders are built on the fly using the labels attached to the emails in the all mail folder.

You see the mail as archived as Google remove the labels, but keeps the mail in the all mail folder. You might want to try some of the settings here https://mail.google.com/mail/u/0/#settings/fwdandpop to see if you can get google to behave as you would like. Perhaps changing the action when the last visible folder is removed might help. But you might have to hide the all mail folder in the Labels section at google https://mail.google.com/mail/u/0/#settings/labels

Look, you're not telling us anything new here. I've been reading these excuses for 19 years. The reality is that Gmail is one the biggest email providers on the planet. No, it's not standard IMAP. Duh. It's Gmail. It's "email +". We all know that, sir. Gmail was not built for Thunderbird's "move message from account A to account B" feature. It's the other way around, Thunderbird was built to serve all email users, including Gmail users. But the feature is broken. It's not moving anything. It's creating duplicate documents in people's accounts, a true management hell for people who mean it when they choose "move" instead of "copy." So don't call it "move" if it's not moving for 30% of the world's inboxes. And please don't tell us we're holding it wrong. The users shouldn't have to do a special dance just because they use a certain email provider.

Including a setting specific for Gmail accounts in Thunderbird settings would solve this problem instantly and save a lot of people from a lot of pain. Thunderbird knows how to delete messages. This situation is not out of Thunderbird's realm of capabilities. All that's needed is a simple checkbox option in the Settings (e.g. "Enable 'True moving' when moving messages from a Gmail account") and then an 'if this, then that action', according to which "move" will mean "copy, archive, and delete" when dealing with Gmail accounts.

There may be simpler, more elegant ways of solving this issue (anything is better than telling users to fuck off). But what do I know, I'm not even a developer, just a dumb Gmail user.

I am not going to debate the topic. It is how it is and as this is a support forum that has to be the starting point of discussion. If you want something else to happen, I suggest you either take your request to the appropriate feedback forum, or file an enhancement bug request.

One thing I do think I need to point out is IMAP itself is not really meant for moving messages from one account to another. That is why messages so often simply don't make the move at all and are lost, not archived as in your use case, but lost. Despite there being a cottage industry in moving mail account data using Thunderbird and IMAP it is actually a rather poor idea for more than a few messages at a time. See https://mzl.la/3SJabHU for reported bugs.

You're right, it's probably not the most commonly used feature, but some people absolutely need it. Moving messages between accounts is one of two reasons that I still have Thunderbird installed (the other one being stripping attachments from Gmail messages).

I have suspected that moving/deleting is bug prone (been paranoid about it since the "delete" bug on the early generations of iPhones, which also archived messages instead of deleting) and have developed perhaps an unnecessarily obsessive protocol for it. I have two Gmail labels in each of the accounts: From Account 1, To Account 1 in one account From Account 2, and to Account 2 in the other. I use Thunderbird to copy the messages to these folders and then verify that everything is correct in the destination account via Gmail in a browser tab. Then I use a second Gmail tab to delete the original messages. It takes like 6 steps when it should only take 1.

I'm happy to post in the feedback forum. Is that under Community or Discussions? Are there subforums or do you just post a thread in https://connect.mozilla.org/t5/discussions/bd-p/discussions ? A bit complicated for an open-source project. I guess that's what happens when a non-profit foundation starts raking in a billion dollars a year in revenue.