JetBrains: Add back GitHub workflow to test Java side of integration

Created by: philipp-spiess

Part of #35787

This brings back the GitHub workflow tests that build the JetBrains extensions and runs some rudimentary checks. We used a similar script in the previous repo: https://github.com/sourcegraph/sourcegraph-jetbrains/blob/main/.github/workflows/build.yml, however this version has a bunch of tasks removed that never worked (also not in the previous repo).

To ensure this does not use a lot of resources, these workflow current only runs on pull requests that change anything inside the client/jetbrains folder. So I do not anticipate any heaver usage compared to the one we had in the previous repo.

Note that this workflow works in isolation to the JavaScript artifacts necessary for full testing. It is intended to only test if the Java plugin compiles without issues and I've went with the GitHub workflow to avoid us having to figure out how to add the right Java versions to our CI systems. We will need to do this at a later point for full featured E2E tests.

For now the plan is to have a separate CI step added in parallel to the VSCode ones that verifies that our JavaScript changes are good.

Test plan

• Green GitHub status