Input System does not work due to a missing "Restart" prompt when receiving changes from Unity Version Control repository, where Input System package gets installed

Reproduction steps:
1. Create a new project with some basic Input System code
2. Change the input backend to Input Manager and restart
3. While the Editor is open change the activeInputHandler field from 0 to 1 in the ProjectSettings.asset file
4. Observe that no prompt shows up to restart and enable Input System backend

Original VCS steps:
1. Create any new project that uses Unity Version Control
2. Remove the “Input System” package if it was automatically installed (Restart the Editor once prompted)
3. In the Unity Version Control Window, “Check in” all pending changes
4. Go to the “Branches” tab in the UVC Window
5. Right-click on the main branch
6. Select “Create child branch…”, name it (e.g. “Test”) and click Create
7. Make sure the current workplace is in the new branch
8. Go to the Package Manager
9. Install “Input System” package (Restart the Editor once prompted)
10. Drag the attached “SimpleInputTest.cs” script into the Project Window
11. Attach that script to any GameObject in the Hierarchy (or create a new empty one)
12. Enter Play mode
13. Press the Spacebar button on the keyboard
14. Observe the Console that input is detected
15. In the UVC Window, “Check in” all pending changes
16. Go to the “Branches” tab again and right-click on the main branch
17. Select “Switch workplace to this branch” (Restart the Editor once prompted)
18. In the “Branches” tab, right-click on the main/Test branch
19. Select “Merge from this branch…” and click “Apply changes”
20. Reload the Scene if prompted
21. Observe that the “Input System” package is now installed
22. Enter the Play mode and press the Spacebar on the keyboard
23. Observe the Console

Expected result: Input System is working and “Spacebar pressed!“ log is visible
Actual result: Input System does not work and “Keyboard.current is null! Input System not initialized correctly yet.” log is visible

Reproducible with: 2022.3.62f1, 6000.0.48f1, 6000.1.3f1, 6000.2.0a10 (1.18.1)

Reproducible on: Windows 11
Not reproducible on: no other environment tested

Notes:

• The Input System works again after a manual restart
• After setting up the UVC, the issue reproduces while also switching workplaces between the branches where the Input System package is installed and where it isn’t
• Issue also reproduces if the project is then opened from Hub - Add > Add from repository