ci: enable new spelling check by updating doc starter pack (canonical#774)

This PR updates Pebble to version 1.3.1 of the [doc starter
pack](https://github.com/canonical/sphinx-docs-starter-pack).

The main change is a new spelling check. I've reorganised our docs CI,
so the most important file to review is `.github/workflows/docs.yaml`.

The other changes follow the latest changed files in the starter pack.
I've taken this opportunity to remove starter pack files that we don't
use in Pebble, to keep things tidy. (I probably originally advocated for
keeping them, but now I think they add noise.)

Author: dwilding

.github/workflows/docs.yaml

@@ -1,42 +1,39 @@
-#
 name: Docs
 
 on:
   push:
     branches:
-      - main
+      - master
   pull_request:
-  workflow_call:
   workflow_dispatch:
 
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref }}
-  cancel-in-progress: true
+permissions: {}
 
 jobs:
-  docchecks:
-    name: Checks
-    runs-on: ubuntu-22.04
-    outputs:
-      linkcheck-result: ${{ steps.linkcheck-step.outcome }}
+  docs-spelling:
+    name: Spelling
+    runs-on: ubuntu-latest
     steps:
-      - name: Checkout
-        uses: actions/checkout@v6
+      - uses: actions/checkout@v6
         with:
-          fetch-depth: 0
-      - name: Python
+          persist-credentials: false
+      - name: Set up Python
         uses: actions/setup-python@v6
         with:
           python-version: "3.12"
-      - name: Links
-        id: linkcheck-step
-        if: success() || failure()
-        uses: canonical/documentation-workflows/linkcheck@main
+      - name: Check spelling
+        run: make -C docs spelling
+
+  docs-linkcheck:
+    name: Links
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v6
         with:
-          working-directory: docs
-      - name: Markdown lint
-        id: markdown-step
-        if: success() || failure()
-        uses: DavidAnson/markdownlint-cli2-action@v16
+          persist-credentials: false
+      - name: Set up Python
+        uses: actions/setup-python@v6
         with:
-          config: "docs/.sphinx/.markdownlint.json"        
+          python-version: "3.12"
+      - name: Check links
+        run: make -C docs linkcheck