feat: Add project foundation, documentation, and Docker setup

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/Dockerfile.prod

@@ -0,0 +1,22 @@
+# Production Dockerfile with pinned image digests
+# golang:1.25.6-alpine
+FROM golang@sha256:d9b2e14101f27ec8d09674cd01186798d227bb0daec90e032aeb1cd22ac0f029 AS builder
+
+WORKDIR /app
+
+COPY go.mod go.sum ./
+RUN go mod download
+
+COPY . .
+RUN CGO_ENABLED=0 GOOS=linux go build -ldflags="-s -w" -o server ./cmd/server
+
+# gcr.io/distroless/static-debian12:nonroot
+FROM gcr.io/distroless/static-debian12@sha256:6dcc833df2a475be1a3d7fc951de90ac91a2cb0be237c7578b88722571f77571
+
+COPY --from=builder /app/server /server
+
+USER nonroot:nonroot
+
+EXPOSE 8080
+
+ENTRYPOINT ["/server"]