The “Input System package (New)” and “Both” options are still present in the Active Input Handling option drop-down menu when the Input System package is uninstalled

Reproduction steps:
1. Open the attached project "ReproProj"
2. Open the “/Assets/Scenes/SampleScene.unity” Scene
3. Open the Package Manager (Window > Package Manager)
4. Uninstall the Input System package
5. Open Player Settings (Edit > Player Settings)
6. In the Other Settings section, observe what is present in the Active Input Handling option drop-down menu

Expected result: The options of the Input System package are not present in the Active Input Handling drop-down menu after uninstalling the package
Actual result: “Input System package (New)” and “Both” options are present

Reproducible with: 1.2.0 (2021.3.31f1), 1.8.0-pre.1 (2021.3.31f1, 2022.3.11f1, 2023.1.16f1, 2023.2.0b13, 2023.3.0a9)

Reproducible on: Windows 10 Enterprise 21H2
Not reproducible on: No other environment tested