[Github] Simplify checkout in docs test workflow (llvm#132975)

This makes things quite a bit simpler and also gets rid of some API
calls. We weren't hitting any API limits, but getting rid of them leaves
more quota for other things should we ever need it. This just diffs the
merge commit in the pull request workflows, which gives the diff for the
PR.

Author: boomanaiden154

.github/workflows/docs.yml

@@ -54,19 +54,17 @@ jobs:
     runs-on: ubuntu-24.04
     if: github.repository == 'llvm/llvm-project'
     steps:
-      # Don't fetch before checking for file changes to force the file changes
-      # action to use the Github API in pull requests. If it's a push to a
-      # branch we can't use the Github API to get the diff, so we need to have
-      # a local checkout beforehand.
-      - name: Fetch LLVM sources (Push)
-        if: ${{ github.event_name == 'push' }}
+      - name: Fetch LLVM sources
         uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
         with:
-          fetch-depth: 1
+          fetch-depth: 2
       - name: Get subprojects that have doc changes
         id: docs-changed-subprojects
         uses: step-security/changed-files@3dbe17c78367e7d60f00d78ae6781a35be47b4a1 # v45.0.1
         with:
+          skip_initial_fetch: true
+          base_sha: 'HEAD~1'
+          sha: 'HEAD'
           files_yaml: |
             llvm:
               - 'llvm/docs/**'
@@ -96,11 +94,6 @@ jobs:
               - 'flang/include/flang/Optimizer/Dialect/FIROps.td'
             workflow:
               - '.github/workflows/docs.yml'
-      - name: Fetch LLVM sources (PR)
-        if: ${{ github.event_name == 'pull_request' }}
-        uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
-        with:
-          fetch-depth: 1
       - name: Setup Python env
         uses: actions/setup-python@42375524e23c412d93fb67b49958b491fce71c38 # v5.4.0
         with: