I've had this issue since iOS18 and subsequently 18.1 and 18.1.1. All the same messages, POSIX96, POSIX54, Cannot connect, Connecting, mailbox already exists etc.
I believe it's all related the iOS UI handling the mapping of mailboxes. Im no expert at all but after being frustrated again today by missing out on business opportunities because mail just doesn't not come through I did some digging. For the third or fourth time I removed and re-added the email account and realized that the UI doesn't seem to save your changes when mapping the mailboxes under Mail settings > account settings > advanced. Or it might look like it has but has actually done something else. There is no save button and you can only back out of the window. If you go forward again and view your changes they have most likely reverted back to they were or for me on this occasion end up a mix of what I had set.
If you then go over to the mail app and change those settings (why can't they all be in one place Apple?) to match your prefix maps they too do not save and or give some very weird results.
If I view my mailboxes (inbox, sent etc) and click edit top right, then tick all the ones I just mapped in 'account settings > advanced' so they show up and are mapped accordingly nothing sticks or it gives weird results. Previously this (while stupidly overly complex) worked but now it does not. This part too causes crashes, corruption and plain weirdness. If I tick sent mailbox for example I can end up with two! If I click on one of them to view what's in the sent mailbox for example the mailbox can actually be the drafts mailbox not sent! Not all the mailboxes/folder under my IMAP prefix appear, sometimes they do, sometimes they don't. Even when they do all appear and I manage to map everything as it should I still get weird results when actually looking in the mailbox. Sometimes it's empty or it will have items from drafts, or sent in a folder that shouldn't.
I believe it's this that's causing the issue. Mail app and the settings app are broken when it comes to mailbox mapping and so mail app is expecting to receive data from the inbox but it either doesn't (because the link is incorrect despite what the settings say) or gets sent data its not expecting and so we get various error messages. It certainly explains the mailbox already exists messages Ive been getting and possibly POSIX54 server not responding.
Just my experience but I think Apple haven't fixed it yet because they're looking in the wrong place and even when you look in the right place not everything is as it seems.