Connect existing Element account to Google/Facebook/etc

On the Element login page, there are various social auth (OpenID Connect) buttons (for matrix.org, Google, Facebook, Github, Gitlab, Apple), but it does not seem to be possible to use these with an existing account: after authenticating with the OIDC provider, I am asked to provide my Matrix username, and if it exists already, I'll just get an error saying the username is not free. That feels like a weird workflow and unlike all other applications that support OIDC.

Start with the Element login flow and the OIDC account behavior described in the issue. Check how existing Matrix usernames are handled after authentication, then define the expected account-linking flow and acceptance cases for the listed providers. No files or tests are named, so locate the relevant client and authentication entry points first.

Written by the indexing model from the issue text.