Not directing to desktop app once a client preference was selected

Nobody has claimed this yet.

### Steps to reproduce

1. I'm trying to follow a matrix.to link and open the destination in my locally installed Desktop client
2. I select Element as client on the matrix.to site
3. The browser offers me to open the locally installed Desktop client (that's great)
4. I click cancel and see a page for Download vs. Continue to browser
5. Going to browser now goes to browser, which I don't want, but that's expected
6. Clicking download goes to download, which I don't want either, but that's also expected
7. How do I now open the desktop client?

When I return to this page later with the next matrix.to link, the preferences have been stored and I see directly the download vs. browser choice. It turns out that the first click on download offers to open the desktop app again, but after that it keeps going to download. This is not clear at all.

### Outcome

#### What did you expect?
Clear button: "Open in Desktop app" next to "Download" and "Browser"

#### What happened instead?
No clear way for the user to trigger the desktop app

See video

https://github.com/user-attachments/assets/c2a53c3b-4380-4671-903b-a82c2743ac1b

Reproduce the matrix.to flow with an installed Element Desktop client, then trace the client-selection and Download/Browser choice entry points. Verify the desktop option remains visible and directly opens the installed app after a preference has been saved; confirm the reported flow no longer requires clicking Download first.

Written by the indexing model from the issue text.