I wonder how this is possible. I have the Tor network middleware installed and all my apps use it.

Tor Browser is special in some ways because the browser itself has some control over the circuits. It shows me the circuit it uses and gives a way to request a new circuit. So at first I thought TB has its own embedded Tor middleware (for lack of a better term). But if I shutdown Tor (systemctl stop tor), then TB does not function. So TB is still dependent on the tor middleware.

Hence why I am baffled that Tor browser does not work over a particular public library wifi connection, but the Tor middleware works fine (including Firefox and other apps that are configured to use the Tor proxy).

How would a library distinguish Tor Browser from a Tor-proxied Firefox?