I also tried just adding the Gmail account to Thunderbird as POP but again, that just downloads all the emails in chunks into the Thunderbird inbox without folders.

POP accounts only download the Inbox. Unless you want to move all messages in folders to Inbox, you need to add the account as IMAP, which syncs all folders. After they are downloaded, copy them to subfolders of Local Folders, confirm the copy, then delete them from the IMAP folders and cancel the account if desired.

Keep in mind that gmail has bandwidth limits: https://support.google.com/a/answer/1071518

Could you tell me how to "tell" Thunderbird not to exceed Gmail's bandwidth limits? Or does Thunderbird know how to do that on its own? (I read the Google Support article you referenced but couldn't see a solution there.)

I'm not aware of a way to set TB to not exceed the limits. For uploading, it's possible to find the size of a folder by having it shown in the Folder Pane Columns, under View/Layout, or in the folder Properties (right-click menu). For downloading, the size of a folder can be shown the same way.

Thank you again, still a question:

Bandwidth limit: I'm a bit confused about this warning. Apparently, Mozilla Thunderbird downloaded all of my Gmail emails (ca. 11 GB) in one or two goes, even though the Google daily limit for IMAP download is 2.5 GB. How could that happen? I also wasn't locked out of Gmail account or anything like that.

Is the size of the folder 11 GB, as shown by the previous reply? Is it downloading all message bodies or just those that are within the limit, and headers only for the rest?

There is no one folder. I have the IMAP connection between Thunderbird and Gmail, so that all the folders appear in Thunderbird just as they are in Gmail. (I have yet to copy the emails of each folder into same-named Local Folders, the next step in your first recommendation post; I will do that, I just wanted to understand a bit first what was going on.)

I thought that your post warning about the bandwidth limit meant that I shouldn't or wouldn't be able to allow Thunderbird to download/mirror all the emails in one go. But yet that worked out just fine. Or did you mean that I shouldn't copy all the folders in one go into Local Folders because that's when the actual downloading happens and not just the IMAP "mirroring" (don't know the right term here)?

I expect that all the folders appear in TB the same as on gmail, and all the headers. But what about the message bodies? If all the folder sizes add up to 11 GB, then maybe all the bodies have been downloaded. I haven't tried this myself, as my gmail account is far below the bandwidth limit. If some folders have headers only, the limits might be applied once you copy to Local Folders. In any case, check that the bodies are present in Local Folders before you delete from the server.

When I open any given folder in TB, the emails are the same as in Gmail, and when I click any email I see both the full header and the message body.

Yeah, that might be right, that the bandwidth limit has to do with the copying into the Local Folders.

I'm sorry for imposing, but in case you know this from the top of your mind (I've tried to look for this):

1. Can I export all the Local Folders in TB (all my emails once I've copied them into folders there) as, say, MBOX file, when I for example get a new computer? So that they would appear in the same way (same folders) in the new computer? I tried to export one folder with a subfolder like this unto my desktop just to try it out: Tools - ImportExportTools NG- Export folder with subfolders (with structure) - but all I got was a file on my desktop of the type "file" when I clicked Properties.

'Export folder' exports the folder as an mbox file; mbox files have no extension (hence of type File), and are named after the folder. You can test the result by renaming the mbox, then importing by right-clicking Local Folders, IET NG, Import mbox file.

If you plan to copy the setup to a new computer, it's possible to copy the Thunderbird folder in ...AppData/Roaming to ...AppData/Roaming on the new computer and retain the same structure and settings. Make sure the version of TB is the same on both computers.