add basic backend

backend/Dockerfile

@@ -0,0 +1,26 @@
+FROM rust:1.87 AS base
+RUN cargo install --locked cargo-chef sccache
+ENV RUSTC_WRAPPER=sccache SCCACHE_DIR=/sccache
+
+FROM base AS planner
+WORKDIR /app
+COPY . .
+RUN cargo chef prepare --recipe-path recipe.json
+
+FROM base AS builder
+WORKDIR /app
+COPY --from=planner /app/recipe.json recipe.json
+RUN --mount=type=cache,target=/usr/local/cargo/registry \
+    --mount=type=cache,target=/usr/local/cargo/git \
+    --mount=type=cache,target=$SCCACHE_DIR,sharing=locked \
+    cargo chef cook --release --recipe-path recipe.json
+COPY . .
+RUN --mount=type=cache,target=/usr/local/cargo/registry \
+    --mount=type=cache,target=/usr/local/cargo/git \
+    --mount=type=cache,target=$SCCACHE_DIR,sharing=locked \
+    cargo build --release
+
+FROM gcr.io/distroless/cc-debian12 AS runner
+WORKDIR /app
+COPY --from=builder /app/target/release/nuchat .
+ENTRYPOINT [ "/app/nuchat" ]