The 'problem' is with IMAP, as it was not designed for uploading. It can be done, but you encounter network issues. I suggest you create a manual filter to do this and be sure to COPY, not move.

I don't understand how I managed to copy twenty thousand messages and now there's a problem? Sometimes I manage to copy a random number and other times I don't...

What filters are you talking about?

The problem is that copying to IMAP is not a consistent, reliable process. It is not uncommon for people to upload and then find some of the content is missing. The idea of a manual filter is that it may assist by regulating the upload slightly.

The problem is not IMAP. When attempting to copy from POP3 to local folders, the same problem occurs...

Ok, that's over my head. Maybe someone else can respond.

When you select a folder and need to eg: copy to eg: Local Folders That means files get opened to access, copy and paste data and in addition if an imap account is involved uploading via internet protocol to server.

It's common for most people to have Anti-Virus settings which scan files that get opened or get uploaded/downloaded and this means the Anti-Virus is intervening in the process and that can cause problems.

I suggest a good starting point would be to access Anti-Virus and switch off scanning of emails. I would also set up an exclusion on your Thunderbird profile name folders to exempt them and all files they contain from scanning. After all even if they do scan, you should not allow AV to auto 'fix' as they have no concept that one text file may contain more than one email - it might contain hundreds. It's too risky on what might transpire.

Or you could simply restart computer in 'Safe Mode with Networking' and then attempt to copy emails. You would need to use an ethernet cable to connect laptop/computer to router.

It's important to rule out if an Anti-Virus is causing a problem as this is a very common issue.

If you want emails from a POP account to be auto moved to an imap account where the email addresses are different. Then you could access the webmail account and set up a Forwarding of emails to other email address. Then emails on one server are simply auto forwarded to another server. Usually, that means they get 'popped' so are sent to Inbox and may be deleted off original server, so do check settings if you want messages retained. The above is not done in Thunderbird - it's done via webmail account.

Uploading via imap usually has different limits from eg: download/sending limits. This is an example of the gmail uploading via imap limits. https://support.google.com/a/answer/1071518?hl=en

It may also depend on where your Thunderbird profiles are located. If in a default location eg: C://Users/username/Appdata/Roaming/Thunderbird/Profiles/Profile name... Then providing Anti-Virus is not interfering all should go ok. But I would always do it in small batches.

However, if you have a Thunderbird profile mail storage in an alternative location such as a OneDrive or Microsoft account or NAS then emails may not be being copied between files within computer they may be being uploaded/synchronised to another device, drive or server.