Synapse admins can delete themselves using the Admin API

This issue has been migrated from [#12719](https://github.com/matrix-org/synapse/issues/12719).

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Hi,
i already asked (https://github.com/Awesome-Technologies/synapse-admin/issues/260) in the Synapse-Admin github. They told me to create an issue here.

Following issue (feature?):

If i log into Synapse-Admin with my admin Account, which uses the Synapse Admin API, i can delete "myself" and get locked out of synapse.
I think in this situation the requirement should be an existing second admin account? Otherwise a selfdelete should not work, if the account is the only admin on the server?

Search the Synapse Admin API implementation for the account-deletion endpoint and its authorization checks. Trace how it determines administrator status and define the behavior for deleting the sole remaining admin; done means the API prevents that lockout while preserving valid deletion behavior, with regression coverage for the case.

Written by the indexing model from the issue text.