Try this:

Go to TB menu > Account Settings > Server Settings and change the Server Name to export.imap.mail.yahoo.com.

Ask Yahoo! They appear limit IMAP accounts to 10,000 emails per folder not Thunderbird. Although working out anything to do with Yahoo is exceedingly difficult because they do not appear believe in documenting their limits or processes. Security through obscurity perhaps.

Export.imap.mail.yahoo.com should not accept any uploads as it only offers export only but in typical Yahoo manner they do not really document what they offer the server for. This is what passes for information about what yahoo does. https://help.yahoo.com/kb/SLN5033.html

This guy worked it out in 2023, that the problem was Yahoo. https://www.abdulqabiz.com/blog/archives/2023/03/04/yahoo-mail-imap-download-limit-issue/

This is the yahoo documentation for this export server https://help.yahoo.com/kb/download-email-yahoo-mail-third-party-sln28681.html which ends with

Need 2-way syncing? Manually change manually IMAP server settings in Yahoo Mail

The two articles are materially identical except for the bread crumb that the export server is not two way syncing by implication by offering a link to two way syncing and the second article saying IMAP "allows 2-way syncing," the first article says use IMAP settings so I really wonder if anyone writing this stuff has a clue. The reditt discussions even allude to the export settings working as a two way sync. Yahoos document however deny that . IMAP archiving really only sort of works at the best of times but leaves people thinking they have a solution. However IMAP is syncronised to the server so no local IMAP account content will survive it's removal from the server. It may be the Yahoo prodict is not really IMAP, but the provider appears reluctant or incapable of actually stating the facts so how it works is a typical guessing game.

This is a Thunderbird topic discussing the issue https://www.reddit.com/r/Thunderbird/comments/v4ydu0/10000_email_limit_via_imap_in_yahoo_email/ This one is Outlook. https://learn.microsoft.com/en-us/answers/questions/4591907/outlook-2013-2016-issue-with-yahoo-10-000-item-inb And this is in yahoo reditt https://www.reddit.com/r/yahoo/comments/vuag6a/new_issue_2022_mayjune_10000_mail_limit_on_imap/

Note that each topic dates from June 2022 when Yahoo first imposed the limit, notified folk is was some sort of aberration, but it has been popping up over and over ever since so I guess it was not a bug but a policy change.

A week ago I was able to export all 54,000 e-mails (c. 54,000 GB) from my Yahoo Inbox into a folder in a hard drive; but now after trying three times the exporting stops at just over 10,000 from my Yahoo sent box. So perhaps Yahoo is blocking it. This so unfair - they are imposing a storage limit, but are not allowing one to export and rescue all ones e-mails. I'm looking to change to Gmail, but will loose all that scientific work and comment because back in 2002 I chose Yahoo. Perhaps if I deleted e-mails up to a certain date, I could then export the rest? - but from the sent box, they were not exported in date order (they were in order from the inbox). Very strange. Chris.