[Bug]: Desktop 6.2.2 not compatible with packaged calls plugin on MM Server 11.9.0

Nobody has claimed this yet.

### Checks before filing an issue

- [x] This issue doesn't reproduce on web browsers (such as in Chrome). If it does, [issue reports go to the Mattermost Server repository](https://github.com/mattermost/mattermost-server/issues).
- [x] I have checked the [issue tracker](https://github.com/mattermost/desktop/issues) and have not found an issue that matches the one I'm filing. This should include closed issues.
- [x] This issue is not a troubleshooting question. Troubleshooting questions go here: https://forum.mattermost.com/c/trouble-shoot/16.
- [x] This issue is not a feature request. You can request features and make product suggestions here: https://mattermost.com/suggestions/.
- [x] This issue reproduces on the most recent [stable version](https://github.com/mattermost/desktop/releases/latest), or the most recent [prerelease version](https://github.com/mattermost/desktop/releases) of the Mattermost Desktop App.
- [x] I have read the [contribution guidelines](https://github.com/mattermost/desktop/blob/master/CONTRIBUTING.md).

### Mattermost Desktop Version

6.2.2

### Operating System

Windows 11

### Mattermost Server Version

11.9.0

### Steps to reproduce

The packaged version of Calls Plugin with 11.9.0 is 1.12.1. When you start a call in a channel or direct message and then try to pop out the call in a new window. If you attempt to do this in a browser the calls plugin functions normally. We had to roll back to calls ver 1.11.6 to get the calls plugin to function normally in the Desktop 6.2.2 client. I am submitting this in the Desktop because the issue only happens in this application not on the web.

### Expected behavior

Clicking on the pop-out button should show the participants in the call and if someone shares their screen it would be displayed on the pop-out window.

### Observed behavior

Instead of properly loading a pop-out window it loads an entire new session of Mattermost with the tabs at the top but with a message saying calls plugin failed to load content.

### Log Output

```shell
Unable to grab logs.
```

### Additional Information

_No response_

Start by reproducing the pop-out flow on Windows 11 with Desktop 6.2.2, Server 11.9.0, and Calls Plugin 1.12.1, then compare it with the working browser behavior and Calls Plugin 1.11.6. No file or test is named, so trace the desktop pop-out window handling first. Done means the pop-out displays participants and shared screens instead of loading a new session with a plugin error.

Written by the indexing model from the issue text.