Add sync engine, web UI, Docker setup, and tests

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Dockerfile.sync

@@ -0,0 +1,15 @@
+FROM python:3.11-slim
+
+RUN apt-get update -qq && \
+    apt-get install -y -q --no-install-recommends git && \
+    rm -rf /var/lib/apt/lists/*
+
+RUN pip install --no-cache-dir requests
+
+# Git identity for commits inside the container
+ENV GIT_AUTHOR_NAME=outline-sync \
+    GIT_AUTHOR_EMAIL=sync@local \
+    GIT_COMMITTER_NAME=outline-sync \
+    GIT_COMMITTER_EMAIL=sync@local
+
+WORKDIR /work