If a user wants to delete their Area 51 account, it's not possible to do so through the normal settings. The account deletion FAQ says to contact SE if one wants their Area 51 account deleted.
When I click the "contact us" link at the bottom of the Area 51 homepage, I get directed to https://area51.meta.stackexchange.com/contact, i.e. the Area 51 Discussions contact form. Area 51 Discussions is based off the "modern" SE code base.
From there, if one tries to choose the option "I need to delete my user profile", the system shows a dialog box with an option to click "Continue" or close the box. If I close the box, the dropdown option is cleared. This is intended behavior on normal SE sites where one can delete their own account, but on Area 51 it doesn't make sense since one can't delete their own account.
Additionally, if one clicks the "Continue" button, they are then redirected to https://area51.meta.stackexchange.com/users/delete/current, which leads to a 404 error.
This creates a very confusing scenario for one who wants to delete their Area 51 account: they can't do so through the normal account settings, then the FAQ says to contact SE, then the contact form doesn't allow one to choose the option for deletion and directs them to a non-existent page instead.
The solutions here would be to remove the restriction against choosing the "I need to delete my user profile" option on the Area 51 Discussions contact form, or to make the Continue button not direct the user anywhere, but just close the box and leave the option set.