feat: add Dockerfile for backend service

Introduced a multi-stage Dockerfile for the backend, enabling streamlined builds and optimized runtime image with Node.js 22.

backend/Dockerfile

@@ -0,0 +1,17 @@
+FROM node:22-slim AS base
+ENV PNPM_HOME="/pnpm"
+ENV PATH="$PNPM_HOME:$PATH"
+RUN corepack enable
+
+FROM base AS build
+WORKDIR /usr/src/app
+COPY . .
+RUN --mount=type=cache,id=pnpm,target=/pnpm/store pnpm install --frozen-lockfile
+RUN pnpm run --filter @memegoat/backend build
+RUN pnpm deploy --filter=@memegoat/backend --prod /app
+
+FROM base AS runtime
+WORKDIR /app
+COPY --from=build /app .
+EXPOSE 3000
+CMD [ "node", "dist/main" ]