Editor unselects elements when entering and then exiting the Play Mode

Reproduction steps:

1. Open the user’s attached project
2. In Hierarchy go to Menu > Song Panel Collapsed
3. In Inspector scroll down to “Time Between Elements” and change the value of it to 0.16
4. Press CTRL + S to save
5. Enter the Play Mode
6. Exit the Play Mode
7. Observe the results

Expected result: “Song Panel Collapsed” Object is still selected in the Hierarchy
Actual result: “Song Panel Collapsed” Object is no more selected

Reproducible with: 2022.1.0b10, 2022.1.17f1, 2023.1.0a1, 2023.1.0a11
Not reproducible with: 2021.3.10f1
Could not test with: 2020.3.40f1,2022.1.0a1 - 2022.1.0b9, 2022.2.0b1, 2022.2.0b8 (NullReferenceException: Object reference not set to an instance of an object
UnityEditor.ProjectBrowser.FrameObject)

Notes:

• Using "Enter Play Mode Options" with "Disable Reload Domain", "Disable Reload Scene" and "Disable Scene Backup"
• Reproduction video is in internal notes “Unity Select Issue - 2022 09 02 13 51 27”
• Could not find the first regressed version due to the errors with alpha/beta versions