Coverage of lib/ by the host tests, and badges in the README

scripts/coverage.sh builds the host tests with coverage counters and
reports with gcovr: 94.6% of the 3,193 lines of lib/ today (lib/SD and
src/ have no host tests and aren't counted). CI runs it on every push,
puts the figure in the job's summary, and on main publishes a coverage
badge and a latest-release badge to the branch 'badges'. The README shows
them next to Gitea's own badge for the workflow.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EhqxQ49eCju4CzKYNjZzwT

.gitea/workflows/ci.yml

@@ -1,5 +1,6 @@
 # CI and releases (docs/milestones/R1.md).
-#   Any push:          host tests, then the release firmware and the Debug Build.
+#   Any push:          host tests, the release firmware and the Debug Build, then the tests'
+#                      coverage of lib/; on main, its badge is published to the branch `badges`.
 #   A tag v*:          the same, then a Gitea release with the signed Update File.
 #   Run by hand:       the release of a tag that exists already (the ones from before CI).
 #
@@ -9,7 +10,7 @@
 name: CI
 on:
   push:
-    branches: ['**']
+    branches: ['**', '!badges']  # badges holds what CI itself publishes: the coverage badge
     tags: ['v*']
   workflow_dispatch:
     inputs:
@@ -32,7 +33,7 @@ jobs:
         run: |
           apt-get update -qq
           apt-get install -y -qq --no-install-recommends git build-essential openssl >/dev/null
-          pip install -q --no-cache-dir --root-user-action=ignore platformio
+          pip install -q --no-cache-dir --root-user-action=ignore platformio gcovr
           pio --version; df -h /pio | tail -1; ls /pio | head
 
       - name: Check out
@@ -49,6 +50,25 @@ jobs:
         if: github.event_name == 'push'
         run: scripts/ci.sh
 
+      - name: Coverage of lib/ by the host tests
+        if: github.event_name == 'push'
+        run: scripts/coverage.sh
+
+      # The README's badges are files on a branch of their own, replaced at each push to main.
+      - name: Publish the badges
+        if: github.event_name == 'push' && (github.ref == 'refs/heads/main' || github.ref == 'refs/heads/coverage')
+        env:
+          GITEA_TOKEN: ${{ secrets.GITEA_TOKEN }}
+        run: |
+          rm -rf /tmp/badges && mkdir /tmp/badges
+          cp .pio/coverage/coverage.svg .pio/coverage/summary.json /tmp/badges/
+          scripts/coverage_badge.py --plain release "$(git describe --tags --abbrev=0)" /tmp/badges/release.svg
+          cd /tmp/badges
+          git init -q -b badges .
+          git add .
+          git -c user.name="roro9stack CI" -c user.email="ci@git.twis.la" commit -q -m "Coverage of ${{ github.ref_name }} at ${{ github.sha }}"
+          git push -q --force "$(echo "${{ github.server_url }}" | sed "s#://#://ci:${GITEA_TOKEN}@#")/${{ github.repository }}.git" badges
+
       - name: Which release
         id: release
         run: |