Unity does not automatically change the window to Game View when pressing Play

To reproduce:
1. Create a new project
2. Set the Enter Play Mode setting to “FullScreen on”
3. Press Play
4. Press Shift+control+F7 to exit the full screen
5. Stop the game
6. Set the Enter Play Mode setting to “Normally” (“Play in Window” in newer versions)
7. Open Scene view
8. Press Play

Expected result: It automatically switches to the Game View window
Actual result: It stays in the Scene View window

Reproducible with: 2022.1.7f1, 2022.2.0a17, 2023.1.0a2
Could not test with: 2020.3.36f1, 2021.3.5f1 (no FullScreen feature)

Reproduced on: macOS 12.4

Note: For clearer reproduction steps, see https://youtu.be/EzXtnVOC2ZE from 1:00