Element Desktop profile authentication callback opens default profile instead of selected profile

### Steps to reproduce

Title:
Login callback ignores --profile and opens default Element profile

Environment:
- Fedora Silverblue
- GNOME Wayland
- Element Desktop tar.gz
- Version: 1.12.26

Steps:
1. Run:
./element-desktop --profile work

2. Login with Matrix account in browser

3. Browser authentication completes

Expected:
The login callback should return to the Element instance started with --profile work.

Actual:
The callback launches/activates the default Element profile.

### Outcome

The URI scheme handler appears to be registered globally and does not preserve the profile argument of the originating instance.

[bug video youtube](https://youtu.be/MCOPtcycKrE)

### Operating system

Fedora Silverblue

### Application version

1.12.26

### How did you install the app?

Element Desktop tar.gz

### Homeserver

matrix.org

### Will you send logs?

No

Start by reproducing the issue with ./element-desktop --profile work, then trace the browser authentication callback and the URI scheme handler to see how the originating profile is passed or lost. Done means completing login from the browser returns to the Element instance using the work profile rather than opening or activating the default profile.

Written by the indexing model from the issue text.