Add Playwright tests for read-only mode

[joelverhagen]

Progress on https://github.com/NuGet/Engineering/issues/4953

We currently use a deprecated test framework for web tests. This starts a migration to use Playwright instead. Note that the current web tests are still enabled. We should only delete them after all of the existing tests are re-implemented to ensure we have proper test coverage.

Summary of changes:

1. Add Playwright tests for ReadOnlyMode
2. Add web UI test package dependency, this allows us to build in VS 2026 without the web UI test dependency.
3. Add a DEV test configuration file to allow the team to run the tests easily, locally. They require access to a team Key Vault so they are not immediately useful to OSS contributors.