Migrate to new vscode testing APIs

[aeisenberg]

Currently, this extension uses the UI test explorer as a ui for testing. However, this extension has recently become deprecated due to the release of native APIs for testing.

We should migrate to this new API. It will simplify our development since this extension would no longer have any dependencies on a third party extension.

Here is a migration guide.

Note that when we change this, we can also change the devcontainer files on the vscode-codeql starter repo to avoid installing the test UI extension by default.

[aeisenberg]

Duplicate of #1085.

[dbartol]

Reopened because #1085 is now more focused on publishing to open-vsx, and moving to the new testing API was just one possible solution.

[dbartol]

#2306 is merged, which enables this under the canary flag. Keeping this issue open until we've enabled the new code unconditionally.

[adityasharad]

We're ready: will inform internal developers first and then switch.

[aeisenberg]

@dbartol Is it time to enable this unconditionally? Considering that we've been using this internally for 8 months with no problems, I think it's safe.

[dbartol]

Yeah, it's definitely time. #3232