Shared links to chats in kde.org rooms don't work

I'm using Element from the browser. I'm in logged-in to KDE's developers room, which is public at: https://webchat.kde.org/#/room/#kde-devel:kde.org

If I select any message and click share, it generates a link that looks like this:

https://matrix.to/#/!cbhzHdSgDDghlosjCd:kde.org/$4XblO9sx7CPHanbS3poE6VCvz3PY8erVbijzenSpmVo?via=matrix.org&via=kde.org&via=im.kde.org

Following this link I'm presented with a screen that lets me select Element as my client, but after doing so I just land at Element's login page (despite me already being logged in) and never at the chat room.

Reproduce the reported matrix.to link from an already logged-in session on webchat.kde.org, then choose Element as the client. Trace where the flow ends after client selection; done means the link opens the referenced KDE room and message without incorrectly showing the login page.

Written by the indexing model from the issue text.