In our experience, the behaviour has been static for some years now and is a little counter intuitive.
TURN connections (Port and Protocol combinations) are all tried but given preference in the order they are defined in ICE config array.
For TCP, if there is a route or NAT path to the TURN server, it will try that before falling back to use a web proxy defined in the browser.
A browser defined proxy does not force the connection via the proxy, so if you need to test a proxy tunnel, block the network egress to the TURN server from the browser in a firewall (on host will do).
The web proxy will only work if:
a) the destination port is defined as allowed to CONNECT in the proxy. This is normally allowed for all TLS ports, so 443 would work, but non common web ports like 3478 may not.
b) the browser has ability to authenticate to the web proxy (if required)
TLS connections use the same logic.
If you must use port 443, consider specifying TLS ( TURNS: protocol) in your ICE config, as some more advanced networks will drop non TLS traffic to common TLS ports.
Cheers,
Warren