Validate local development scenarios in CI

[MackinnonBuck]

Adds a check to ensure that local development scenarios are not broken:

• Build and pack (Debug)
• Build and pack (Release)
• Run project template tests
  • These depend on the locally built shared framework being available
  • Currently all project template tests are run, but we could speed up this check a bit by limiting this to a smaller subset of tests (e.g., Blazor tests only)

This check can be further extended with additional scenarios as we see fit.

Fixes #56237

[MackinnonBuck]

Looks like we're required to specify a minor and patch version when installing the JDK. This is hardcoded right now, as it is in helix. See also: #57476

[wtgodbe]

LGTM, but can you run an internal build against this branch to confirm the ci.yml changes didn't bust anything? Just push the branch to https://dev.azure.com/dnceng/internal/_git/dotnet-aspnetcore & queue a build of https://dev.azure.com/dnceng/internal/_build?definitionId=21 against that branch

[MackinnonBuck]

The internal build passed; I'm going to merge this now.