[Bug]: Full screen does not persist when both player and window is in full screen

### Guidelines

- [x] I have encountered this bug in the [latest release of FreeTube](https://github.com/FreeTubeApp/FreeTube/releases).
- [x] I have encountered this bug in the [official downloads of FreeTube](https://github.com/FreeTubeApp/FreeTube#official-downloads).
- [x] I have [searched the issue tracker for open and closed issues](https://github.com/FreeTubeApp/FreeTube/issues?q=is%3Aissue+sort%3Arelevance-desc) that are similar to the bug report I want to file, without success.
- [x] I have searched the [documentation](https://docs.freetubeapp.io/) for information that matches the description of the bug I want to file, without success.
- [x] This issue contains only one bug.
- [x] I have read and agree to follow the [rules](https://docs.freetubeapp.io/community/rules/).

### Describe the bug

1. Full screen the window e.g. F11
2. Full screen the player, either through the button or the F hotkey
3. Close the app e.g. Ctrl+Q or Alt+F4
4. Open the app again and see that app unfortunately doesn't launch in full screen

### Expected Behavior

App should open in full screen

### Issue Labels

inconsistent behavior

### FreeTube Version

v0.23.13-nightly-6941 Beta

### Operating System Version

Windows 11 IoT Enterprise LTSC 24H2

### Installation Method

.exe

### Primary API used

Local API

### Last Known Working FreeTube Version (If Any)

Commits before https://github.com/FreeTubeApp/FreeTube/commit/8bc581c387e3dfb82cacb608000b36db9a6d4d9c

### Additional Information

_No response_

### Nightly Build

- [x] I have encountered this bug in the latest [nightly build](https://docs.freetubeapp.io/development/nightly-builds).

No source file, test, or entry point is named. Reproduce the Windows 11 sequence with window fullscreen followed by player fullscreen, then trace the app's fullscreen state restoration; done means reopening after both states were active starts the app in fullscreen.

Written by the indexing model from the issue text.