I am trying to understand what it is that has become corrupted? If it's just the settings that have been messed up, AOL helpdesk or an online page from AOL should be available to help you get those back. That's just a matter of entering the correct server settings. As you're using IMAP, you should not need to restore anything, all your folders are still available on the server.
There is an explanation here on how to retrieve locally stored folders using Time Machine, but I suspect that this is not what you need:
https://www.macworld.com/article/231...-in-macos.html If you restore a folder this way, your settings for the account would still prevent you using the Apple Mail functions on your AOL e-mail.
First, have a look here and note the IMAP settings:
https://help.aol.com/articles/how-do...ve-my-aol-mail I guess Apple Mail is not a commonly used Mail program in AOLs eyes as they do not provide any explanation for that.
There is an extensive explanation on how to set up AOL in Apple Mail here:
https://www.lifewire.com/access-your...e-mail-2260068
I would suggest removing existing AOL settings by selecting 'Mail' - 'Accounts' from within the Mail app, and removing the line that corresponds to your AOL mailbox (select and click on the minus sign at the bottom). Do this first, then follow the steps above to add a new account.