Remove unneeded core code and dependencies

[mrlacey]

Is your feature request related to a problem? Please describe.

There is lots of code left over from the migration from CoreTemplateStudio that is no longer needed. This code includes dependencies that are not used. It also makes testing more complicated--especially as relates to some of the more flakey tests.

Removing the things that aren't needed (and related tests) will make changes faster, reduce some of the current maintenance overhead, hopefully make external contributions easier, and avoid future issues similar to #4491

Describe the solution you'd like

Remove the things that are no longer needed. This will reduce dependencies and simplify testing.

Describe alternatives you've considered

keep things as they are. Possibly with the argument that "we may need them in the future"

Additional context

This was always on my personal "one day it would be nice to..." list, but never formally documented here.

Applies to the following platforms:

• [ ] WinUI
• [ ] WPF
• [ ] UWP