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/Dockerfile

@@ -0,0 +1,27 @@
+# Build stage: the server is pure Go (lib/pq is pure Go), so CGO is off and the
+# result is a static binary that runs on a shell-less base image.
+FROM golang:1.26-alpine AS build
+
+WORKDIR /src
+COPY go.mod go.sum ./
+RUN go mod download
+COPY *.go ./
+
+ARG TARGETOS
+ARG TARGETARCH
+RUN CGO_ENABLED=0 GOOS=${TARGETOS:-linux} GOARCH=${TARGETARCH} \
+    go build -trimpath -ldflags="-s -w" -o /prompt-sync .
+
+# Runtime stage: distroless has no shell, so the binary does its own
+# healthcheck (see -healthcheck in main.go). Runs as non-root.
+FROM gcr.io/distroless/static-debian12:nonroot
+
+COPY --from=build /prompt-sync /prompt-sync
+
+ENV PROMPT_SYNC_ADDR=:8080
+EXPOSE 8080
+
+HEALTHCHECK --interval=30s --timeout=3s --start-period=5s --retries=3 \
+    CMD ["/prompt-sync", "-healthcheck"]
+
+ENTRYPOINT ["/prompt-sync"]