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/run_docs_checks.yml

@@ -0,0 +1,68 @@
+# Generated from xtask::workflows::run_docs_checks
+# Rebuild with `cargo xtask workflows`.
+name: run_docs_checks
+env:
+  CARGO_TERM_COLOR: always
+  RUST_BACKTRACE: '1'
+  CARGO_INCREMENTAL: '0'
+on:
+  pull_request:
+    branches:
+    - '**'
+    paths:
+    - docs/**
+    - crates/docs_preprocessor/**
+  push:
+    branches:
+    - main
+    - v[0-9]+.[0-9]+.x
+    paths:
+    - docs/**
+    - crates/docs_preprocessor/**
+jobs:
+  check_docs:
+    if: github.repository_owner == 'zed-industries'
+    runs-on: namespace-profile-8x16-ubuntu-2204
+    steps:
+    - name: steps::checkout_repo
+      uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683
+      with:
+        clean: false
+    - name: steps::setup_cargo_config
+      run: |
+        mkdir -p ./../.cargo
+        cp ./.cargo/ci-config.toml ./../.cargo/config.toml
+      shell: bash -euxo pipefail {0}
+    - name: steps::cache_rust_dependencies
+      uses: swatinem/rust-cache@9d47c6ad4b02e050fd481d890b2ea34778fd09d6
+      with:
+        save-if: ${{ github.ref == 'refs/heads/main' }}
+    - name: run_docs_checks::lychee_link_check
+      uses: lycheeverse/lychee-action@82202e5e9c2f4ef1a55a3d02563e1cb6041e5332
+      with:
+        args: --no-progress --exclude '^http' './docs/src/**/*'
+        fail: true
+    - name: steps::setup_linux
+      run: ./script/linux
+      shell: bash -euxo pipefail {0}
+    - name: steps::install_mold
+      run: ./script/install-mold
+      shell: bash -euxo pipefail {0}
+    - name: run_docs_checks::install_mdbook
+      uses: peaceiris/actions-mdbook@ee69d230fe19748b7abf22df32acaa93833fad08
+      with:
+        mdbook-version: 0.4.37
+    - name: run_docs_checks::build_docs
+      run: |
+        mkdir -p target/deploy
+        mdbook build ./docs --dest-dir=../target/deploy/docs/
+      shell: bash -euxo pipefail {0}
+    - name: run_docs_checks::lychee_link_check
+      uses: lycheeverse/lychee-action@82202e5e9c2f4ef1a55a3d02563e1cb6041e5332
+      with:
+        args: --no-progress --exclude '^http' 'target/deploy/docs'
+        fail: true
+    timeout-minutes: 60
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref_name }}-${{ github.ref_name == 'main' && github.sha || 'anysha' }}
+  cancel-in-progress: true