Use gh workflow for tests (#41384)

Follow up for: #41304

Splits CI tests (cherry-picks and PRs only for now) into separate
workflows using `gh-workflow`. Includes a couple restructures to
- run more things in parallel
- remove our previous shell script based checking to filter tests based
on files changed, instead using the builtin `paths:` workflow filters


Splitting the docs/style/rust tests & checks into separate workflows
means we lose the complete summary showing all the tests in one view,
but it's possible to re-add in the future if we go back to checking what
files changed ourselves or always run everything.

Release Notes:

- N/A *or* Added/Fixed/Improved ...

---------

Co-authored-by: Conrad <conrad@zed.dev>

.github/workflows/release_nightly.yml

@@ -49,6 +49,9 @@ jobs:
       uses: actions/setup-node@49933ea5288caeca8642d1e84afbd3f7d6820020
       with:
         node-version: '20'
+    - name: steps::clippy
+      run: ./script/clippy
+      shell: bash -euxo pipefail {0}
     - name: steps::cargo_install_nextest
       run: cargo install cargo-nextest --locked
       shell: bash -euxo pipefail {0}
@@ -81,6 +84,9 @@ jobs:
       uses: actions/setup-node@49933ea5288caeca8642d1e84afbd3f7d6820020
       with:
         node-version: '20'
+    - name: steps::clippy
+      run: ./script/clippy.ps1
+      shell: pwsh
     - name: steps::cargo_install_nextest
       run: cargo install cargo-nextest --locked
       shell: pwsh