* Element has to query your server to find out what authentication mechanisms are available before you log in. Therefore if its config points to the default matrix.org homeserver, you end up pinging that every time you log in, even if your homeserver is elsewhere. The solution for now is to change your default homeserver in the config to avoid this.
The same applies to the identity lookup server as well as the homeserver: the app checks the one in your config to ensure that it exists before the user tries to log in on it. It does this with a single request (a GET to https://vector.im/_matrix/identity/api/v1). There is no token exchange there.
The workaround is to configure the app with the correct default homeserver & identity server (if any) for your deployment. The underlying bug (i.e. don't validate the config until the user tries to log in) is https://github.com/vector-im/element-web/issues/11655, and it simply hasn't got to the top of the list yet; we've been focusing on narrowing the UX gap between Element & Discord/Slack/Teams rather than reimplementing the login flows. As you can see on the bug, it's been picked up off the backlog 9 days ago and is currently being worked on.
Separately, I'm seeing a related bug that Element Web's guest mode is incorrectly kicking in on the login page. Guest mode exists so you can deeplink straight to something like https://app.element.io/#/room/#matrix-dev:matrix.org and read scrollback without needing to register an account - but it looks like we're spinning up guests on the default homeserver needlessly on the login page. This is https://github.com/vector-im/element-web/issues/11533, and we've put it on the radar too.
TL;DR: this is slightly leaky, but is it really any different to Chrome's default config loading up Google as a default homepage? Or Firefox loading up Mozilla.org? Or Thunderbird loading up Thunderbird.org? Eitherway, we'll fix the behaviour, but PLEASE understand that this is a million miles away from the bogus "central authority can have influence on another server" smear from the original post.