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/script_checks.yml

@@ -1,21 +0,0 @@
-name: Script
-
-on:
-  pull_request:
-    paths:
-      - "script/**"
-  push:
-    branches:
-      - main
-
-jobs:
-  shellcheck:
-    name: "ShellCheck Scripts"
-    if: github.repository_owner == 'zed-industries'
-    runs-on: namespace-profile-2x4-ubuntu-2404
-
-    steps:
-      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4
-      - name: Shellcheck ./scripts
-        run: |
-          ./script/shellcheck-scripts error