Add SyncPlay stats-for-nerds page, manual sync button, and release pipeline

Phase 0 scaffold plus everything since: quality negotiation, host-relay,
and active drift correction were each built and reverted after real bugs
in live use (see PLAN.md for the full account of each). What remains is
read-only SyncPlay observability (live drift/playback stats page) and a
one-shot manual "sync me to group" action, plus Phase 5 packaging/release
tooling (build.yaml, manifest.json generator, Gitea Actions release
workflow) to distribute it as a proper plugin repository.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

.github/workflows/build.yml

@@ -0,0 +1,29 @@
+name: Build Check
+
+on:
+  push:
+    branches: [ master ]
+  pull_request:
+    branches: [ master ]
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+
+      - name: Setup .NET
+        uses: https://github.com/actions/setup-dotnet@v4
+        with:
+          dotnet-version: '9.0.x'
+
+      # Same private-assembly fetch as release.yml -- see PLAN.md "Known friction / risks".
+      - name: Fetch private SDK references
+        run: |
+          mkdir -p lib/jellyfin-10.11.6
+          docker create --name jf-extract linuxserver/jellyfin:10.11.6
+          docker cp jf-extract:/usr/lib/jellyfin/bin/Emby.Server.Implementations.dll lib/jellyfin-10.11.6/
+          docker rm jf-extract
+
+      - name: Build
+        run: dotnet build src/JellyfinSyncPlus/JellyfinSyncPlus.csproj -c Release