.github: Cleanup actions

Cleanup the .github actions:

- Use the same syntax and/or commands where possible
- Drop unnecessary parameters and steps / commands
- In the all-green job ensure that all CI jobs passed
- Update the naming of jobs
- Review permissions and grant write permission only where
  necessary (repo is set to read-only by default)
- Review installed dependencies (try to fix the failing docs job)
- Run yamllint and fix findings
- Replace deprecated set-output syntax

Signed-off-by: Felix Matouschek <fmatouschek@redhat.com>

.github/workflows/extra-docs-linting.yml

@@ -1,24 +1,21 @@
-name: Lint extra docsite docs and links
+---
+name: Lint docs
+# yamllint disable-line rule:truthy
 on:
-  # Run CI against all pushes (direct commits, also merged PRs), Pull Requests
   push:
     branches:
       - main
-      - stable-*
   pull_request:
   # Run CI once per day (at 06:00 UTC)
-  # This ensures that even if there haven't been commits that we are still testing against latest version of ansible-test for each ansible-base version
+  # This ensures that even if there haven't been commits that we are still
+  # testing against latest version of ansible-test for each ansible-base version
   schedule:
-    - cron: '0 6 * * *'
+    - cron: "0 6 * * *"
 
 jobs:
-  docsite:
-    name: Lint extra docsite docs and links
-    permissions:
-      contents: read
+  linter:
     runs-on: ubuntu-latest
     steps:
-
       - name: Check out code
         uses: actions/checkout@v4