C# doctor: can not use both the net 11 and net 10 track in different projects

[haileymck]

1. open C# doctor with a global json targetting net 11 project
2. update to make C# doctor happy (in my case it was to install net 11 rc 1)
3. run dotnet --list-sdks and see 11.0.100-rc.1.26425.128
4. open different project in C# doctor that has a net 10 global json
5. get

6. I know I have net 10.0.400 but C# doctor updated my environment variables such that it doesn't find it

7. I run dotnet --list-sdks and see the same one and only 11.0.100-rc.1.26425.128

C# doctor must work in both scenarios. Furthermore the tooling requirements in this situation is not helpful
CDK version
Version
11.1.1

[haileymck]

I think that this bug was related to the same instance of VS Code or something ebcause it doesnt reproduce later