Cache the DTE instance in VSSolution Manager, prefer using IVsSolution to retrieve solution file, solution directory and solution open information

[nkolev92]

Bug

Fixes: NuGet/Home#11902

Regression? Last working version:

Description

The DTE service is used quite frequently during the solution initialization (about once per project usually).
This service doesn't change and as such it can be cached. This is another part of https://github.com/NuGet/Client.Engineering/issues/1374

This retrieval accounts for 8% of the initialization of a test lab solution.

In addition to caching the DTE service, we'll use IVsSolution over DTE service where appropriate (there's a bunch of usages of DTE remaining. They'll be handled in a future PR).

Note that while we do have a field for the IVsSolution, there's no guarantee that InitializeAsync of VSSolutionManager has run by the time the methods that were changed were called, so I just switched it to an async lazy to avoid race conditions.

PR Checklist

• PR has a meaningful title

• PR has a linked issue.

• Described changes

• Tests

  • Automated tests added
  • OR
  • Test exception - These scenarios are included in E2E/manual tests.
  • OR
  • N/A

• Documentation

  • Documentation PR or issue filled
  • OR
  • N/A

[nkolev92]

cc @davkean

Hoping you can take a look at this.

After this, I'll work on changing GetAllEnvDTEProjectsAsync to use IVsSolution instead of the DTE.