Time Machine Backup Destination Sharing

I have a Mac mini and now a MacBook, both running MacOS 14. I have an external disk attached to the Mini that I had been using for Time Machine backups, but have been unable to use it for Time Machine backups from the MacBook.

I have used File Sharing options on the Mini to share the external disk and designate it as a "Time Machine backup destination" in the file sharing options. When I go to the MacBook Time Machine settings and select "add backup disk", my Time Machine backup disk attached to the Mini shows up, that's great, but if I select it and try to "set it up" I cannot get through the security steps.

To connect as a "registered user" on the mini, it offers a user/password prompt. I give it to the proper password for my account on the mini, and then it says that I do not have the necessary permissions on the network volume. I know that I am passing the login part, because I can intentionally mistype the password and it will just prompt me to re-enter it. This the account that I am successfully using for Time Machine backups on the mini, it has admin privileges, so what can be the problem?

The Mac mini is connected to the network and to the internet using both wired ethernet and wifi. The MacBook is connected via wifi only, using the same wifi as the mini.