Looking on the Apple Community Site, moving mailboxes seems to be a continuing issue with few remedies of which some don’t work. I have recently run into this issue. Here is what worked for me in Ventura:
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If you have moved mailboxes (folders) to Favorites and try to move them around after selecting them under Favorites it will not work. You can only move mailboxes around by selecting them in the actual account or under “On My Mac” in the account listings, but not under favorites. Not user friendly but that is how it works. Example. I added “On My Mac” to Favorites as it is a more convenient place to access it. I I could not move any folder to another folder when selected under Favorites. But it worked fine by choosing “On My Mac” where listed below with other accounts, including moving between accounts.
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Mailboxes can’t be moved if there are special characters in the mailbox name. For instance some of my mailbox names contained a hyphen “-”. They could not be moved to another mailbox location with the hyphen in the mailbox name. The workaround, other than removing the hyphen is to create a new mailbox by the same name at the desired location then drag the mails inside or cut and paste them to the new location. The delete the now empty mailbox.