Adjacent projects using LibMan delete each other's downloads

[spencer-wcri]

Describe the bug

I have two adjacent projects using LibMan.
When I save one libman.json, it delete the restored files in my other project that uses libman.

To Reproduce

Here's a demonstration repo https://github.com/spencer-wcri/libmanconflict

Expected behavior

Adjacent LibMan projects should be independent. Restoring one should not affect the other.

Additional context

Versions

• Visual Studio: 17.14.16
• .NET: 9.0
• Microsoft.Web.LibraryManager.Build: 3.0.71

Microsoft Library Manager does not appear in my Visual Studio installed products version list.

This seems similar to #667 and #638