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.

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AGENTS.md

@@ -42,9 +42,12 @@ clicking an item copies it back to the clipboard.
   code and server URL in `UserDefaults` (`sync.code`, `sync.serverURL`,
   `sync.version`), pushes the whole store as JSON, and polls every 5s.
 - `Server/main.go` — the Go sync backend (single file, `net/http` + `lib/pq`).
-  Also ships `Server/README.md` (self-hosting) and `Server/prompt-sync.service`
-  (systemd unit). Logs one line per request, creates its schema on startup, and
-  shuts down gracefully on SIGTERM so a redeploy cannot cut off a push.
+  Also ships `Server/Dockerfile` + `Server/docker-compose.yml` (Postgres +
+  server), `Server/README.md` (self-hosting), and `Server/prompt-sync.service`
+  (systemd unit). Logs one line per request, creates its schema on startup,
+  shuts down gracefully on SIGTERM so a redeploy cannot cut off a push, and
+  supports `-healthcheck` (pings local `/healthz`) so the distroless image
+  needs no shell for its Docker `HEALTHCHECK`.
 
 ## Sync protocol