Add a Dockerfile so the sync server is one command to deploy

Self-hosting meant building the binary by hand and wiring Postgres up
yourself. The image is a static binary on distroless with a built-in
healthcheck flag, and docker-compose brings up Postgres alongside it.

The image itself is unbuilt here: no container runtime is available in
this environment, so only the static Linux build and the healthcheck
flag have been exercised.

💘 Generated with Crush

Assisted-by: Crush:kimi-k3

Server/docker-compose.yml

@@ -0,0 +1,37 @@
+# Postgres + the sync server. `docker compose up -d` is the whole deploy:
+#
+#   POSTGRES_PASSWORD=$(openssl rand -hex 16) docker compose up -d
+#
+# Then point the app at http://<host>:8080. The data lives in the named volume,
+# so `docker compose down` keeps it and `down -v` wipes it.
+
+services:
+  db:
+    image: postgres:18-alpine
+    environment:
+      POSTGRES_DB: prompt_sync
+      POSTGRES_USER: prompt
+      POSTGRES_PASSWORD: ${POSTGRES_PASSWORD:?set POSTGRES_PASSWORD}
+    volumes:
+      - prompt-db:/var/lib/postgresql/data
+    healthcheck:
+      test: ["CMD-SHELL", "pg_isready -U prompt -d prompt_sync"]
+      interval: 5s
+      timeout: 5s
+      retries: 10
+    restart: unless-stopped
+
+  server:
+    build: .
+    environment:
+      PROMPT_SYNC_ADDR: ":8080"
+      PROMPT_SYNC_DATABASE_URL: postgres://prompt:${POSTGRES_PASSWORD:?set POSTGRES_PASSWORD}@db:5432/prompt_sync?sslmode=disable
+    ports:
+      - "8080:8080"
+    depends_on:
+      db:
+        condition: service_healthy
+    restart: unless-stopped
+
+volumes:
+  prompt-db: