mail cannot save information about your mailboxes because there isn't enough space

Thank you for your reply. Before we go deleting folders, have a look in System Settings - General - Storage and have a look at Mail and see how much storage it's taking up.

Also are you using a restricted user account or network account that might be restricting storage on your Mac?

Is there a second account on the mac taking up storage space?

If you really want to delete the hidden mail folder. Go to the Finder, hold down the option key ( or Alt key depending on keyboard) then click on GO in the menu bar, then click on Library. In the library folder, find a folder called Mail. In that folder there will be some sub folders V something, mine say V2 and V10. Before moving the files make sure Mail is not running, then move the V folders to the bin ( trashcan) but don't delete. Open Mail and see if it has reverted to the setup stage, fill out your details and see what happens. If all is work Ok empty the trashcan (bin).

The error message you're encountering with Mac Mail is likely related to the lack of available space on your Home folder. Do you know if you have particularly large email inbox and outbox that might exceed the 500GB? Do you have 500GB worth of attachments associated with your emails. I only ask as Mac mail downloads all emails a keeps them in a hidden folder in your user's Library. Mail might have calculated that you might not have enough space to have your complete emails + attachments in your user Library plus all the other data required to use your mac. Are you able to login to a web portal for your emails and see the size of your inbox?