'The type or namespace name 'X' does not exist in the namespace 'Y' ' errors are thrown when a 3D HDRP project is opened after deleting the PackageCache folder

How to reproduce:
1. Open a new 3D Sample Scene (HDRP) project
2. Close the project
3. In the project directory, navigate to the Library folder
4. Delete, the PackageCache folder
5. Open the project
6. Observe the Console

Expected result: No errors are seen
Actual result: Errors can be seen

Reproducible with: 2022.2.0b10, 2022.3.8f1, 2023.1.10f1, 2023.2.0b6, 2023.3.0a2
Not reproducible with: 2021.3.29f1, 2022.2.0b9

Reproducible on: macOS 13.5 (Intel), Windows 10
Not reproducible on: No other environment tested