Edge extension v2025.10.1 SSO login process broken

### Steps To Reproduce

Enter email address
Click Use single sign-in button
Authenticate via IdP
Process hangs once the Bitwarden extension is opened in a new window

### Expected Result

Enter email address
Click Use single sign-in button
Authenticate via IdP
Be logged in

### Actual Result

Enter email address
Click Use single sign-in button
Authenticate via IdP
The extension opens a new window and fails to load.

### Screenshots or Videos

### Additional Context

Attempting to open the extension in a new window fails to load regardless of the login state of the extension.

### Operating System

Windows

### Operating System Version

_No response_

### Web Browser

Microsoft Edge

### Browser Version

142.0.3595.53

### Environment Versions

Version: 2025.10.1

SDK: 'main (d0262d3)'

Server version: 2025.10.2

### Issue Tracking Info

- [x] I understand that work is tracked outside of Github. A PR will be linked to this issue should one be opened to address it, but Bitwarden doesn't use fields like "assigned", "milestone", or "project" to track progress.

No source file or test is named. Reproduce the SSO flow in Microsoft Edge on Windows with extension version 2025.10.1, then trace the extension's authentication and new-window loading entry points. Done means the new window loads and the user is logged in after IdP authentication.

Written by the indexing model from the issue text.