Add app scaffold and workflows

app/backend/Dockerfile

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+#
+# BACKEND DOCKERFILE
+#
+# Multi-stage image for the FastAPI + LiveKit Agent backend using uv.
+# - production: smallest runtime image with gunicorn/uvicorn worker
+# - development: hot-reload friendly image with full toolchain
+# - builder: installs dependencies once for reuse across stages
+#
+# Keep dependency definitions aligned with docs/architecture.md.
+
+FROM python:3.12-slim AS base
+
+ENV PYTHONDONTWRITEBYTECODE=1 \
+    PYTHONUNBUFFERED=1 \
+    PIP_NO_CACHE_DIR=1 \
+    PIP_DISABLE_PIP_VERSION_CHECK=1 \
+    UV_PROJECT_ENVIRONMENT=/app/.venv \
+    UV_LINK_MODE=copy
+
+RUN apt-get update \
+    && apt-get install -y --no-install-recommends \
+        build-essential \
+        curl \
+        libpq-dev \
+    && rm -rf /var/lib/apt/lists/*
+
+RUN groupadd --system app && useradd --system --home /app --gid app app
+WORKDIR /app
+
+# Install uv globally so subsequent stages share the toolchain.
+RUN pip install --upgrade pip uv
+
+# ------------------------------------------------------------------------------
+# Builder: install prod dependencies into an in-project virtualenv
+# ------------------------------------------------------------------------------
+FROM base AS builder
+
+COPY . .
+RUN test -f pyproject.toml || (echo "pyproject.toml is required for uv sync"; exit 1)
+RUN if [ -f uv.lock ]; then \
+      uv sync --frozen --no-dev --compile-bytecode; \
+    else \
+      uv sync --no-dev --compile-bytecode; \
+    fi
+
+# ------------------------------------------------------------------------------
+# Production: minimal runtime image with gunicorn as the entrypoint
+# ------------------------------------------------------------------------------
+FROM python:3.12-slim AS production
+
+ENV PYTHONDONTWRITEBYTECODE=1 \
+    PYTHONUNBUFFERED=1 \
+    PIP_NO_CACHE_DIR=1
+
+RUN apt-get update \
+    && apt-get install -y --no-install-recommends libpq5 \
+    && rm -rf /var/lib/apt/lists/*
+
+RUN groupadd --system app && useradd --system --home /app --gid app app
+WORKDIR /app
+
+COPY --from=builder --chown=app:app /app /app
+ENV PATH="/app/.venv/bin:$PATH"
+
+USER app
+EXPOSE 8000
+CMD ["gunicorn", "-w", "4", "-k", "uvicorn.workers.UvicornWorker", "main:app", "--bind", "0.0.0.0:8000"]
+
+# ------------------------------------------------------------------------------
+# Development: includes dev dependencies and keeps uvicorn reload-friendly
+# ------------------------------------------------------------------------------
+FROM base AS development
+
+COPY . .
+RUN test -f pyproject.toml || (echo "pyproject.toml is required for uv sync"; exit 1)
+RUN if [ -f uv.lock ]; then \
+      uv sync --frozen --dev --compile-bytecode; \
+    else \
+      uv sync --dev --compile-bytecode; \
+    fi
+
+ENV PATH="/app/.venv/bin:$PATH"
+USER app
+EXPOSE 8000