Editor doesn't build a project when "Install into source code 'build' folder" is enabled after switching projects

How to reproduce:

1. Download both user-attached projects from (projectA.zip) file
2. Download and build the Unity Editor for Linux and the LinuxPlayer from source
3. Open “ProjectA“
4. In the BuildSettings enable “Install into source code 'build' folder“ option and build and run the project
5. Observe the text in the player window
6. Close the player and project and open “ProjectB“
7. Repeat steps 4 and 5

Expected results: the text in the second player window says “Project B“ which is different when compared with the previous project’s build

Actual results: the text in the second player window says “Project A“ which is the same as in the previous project’s build

Reproducible with: 2021.3.5f1

Could not test with: 2023.1.0a5 (no “Install into source code 'build' folder“ option in the BuildSettings window)

Reproducible on: Ubuntu 20.04