Do Mastodon's internal tools allow administrators to circumvent 2FA?
Not directly. You can do it with access to the instance's Postgres database, but I'd expect relatively few instance admins (as opposed to instance owners) to have that; the admin tools don't include a database console, and you can't use a credential for the admin tools to authenticate to the database.
Then check your mail server for outgoing mail, and use the mail sent to the user to change the password.
If you are the instance owner you can do whatever you want. Additionally, many instances are installed on a single host (https://masto.host) and almost all instances are on VPS in various managed clouds.