feat: add FastAPI backend with PostgreSQL and start script fixes

- Add server/ directory with FastAPI backend
- Fix server/start.sh to properly handle venv on Windows/Git Bash
- Add alembic migrations and pyproject.toml
- Add server tests

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

start.sh

@@ -2,6 +2,150 @@
 set -euo pipefail
 
 SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
-cd "$SCRIPT_DIR/web"
+ENV_FILE="$SCRIPT_DIR/.env"
+ENV_EXAMPLE_FILE="$SCRIPT_DIR/.env.example"
+MODE="${1:-all}"
 
-exec ./start.sh
+RED='\033[0;31m'
+GREEN='\033[0;32m'
+YELLOW='\033[1;33m'
+NC='\033[0m'
+
+info()  { echo -e "${GREEN}[INFO]${NC} $*"; }
+warn()  { echo -e "${YELLOW}[WARN]${NC} $*"; }
+error() { echo -e "${RED}[ERROR]${NC} $*"; exit 1; }
+
+if [ ! -f "$ENV_FILE" ]; then
+  if [ -f "$ENV_EXAMPLE_FILE" ]; then
+    warn ".env not found. Creating it from .env.example"
+    cp "$ENV_EXAMPLE_FILE" "$ENV_FILE"
+  else
+    error ".env and .env.example are both missing."
+  fi
+fi
+
+set -a
+. "$ENV_FILE"
+set +a
+
+SERVER_STARTUP_TIMEOUT="${SERVER_STARTUP_TIMEOUT:-300}"
+SETUP_COMPLETED="${SETUP_COMPLETED:-false}"
+
+prepare_web() {
+  info "Preparing web dependencies..."
+  (
+    cd "$SCRIPT_DIR/web"
+    ./start.sh deps
+  )
+}
+
+prepare_server() {
+  info "Preparing server dependencies..."
+  (
+    cd "$SCRIPT_DIR/server"
+    ./start.sh deps
+  )
+}
+
+start_web() {
+  prepare_web
+  cd "$SCRIPT_DIR/web"
+  exec ./start.sh start
+}
+
+start_server() {
+  prepare_server
+  cd "$SCRIPT_DIR/server"
+  exec ./start.sh start
+}
+
+start_setup_web() {
+  warn "Initial setup is not completed. Starting web only."
+  warn "Finish the setup form first. After setup is saved, run ./start.sh again to launch FastAPI as well."
+  prepare_web
+  cd "$SCRIPT_DIR/web"
+  exec ./start.sh start
+}
+
+start_all() {
+  local server_pid=""
+
+  prepare_web
+  prepare_server
+
+  cleanup() {
+    if [ -n "$server_pid" ] && kill -0 "$server_pid" 2>/dev/null; then
+      warn "Stopping FastAPI server..."
+      kill "$server_pid" 2>/dev/null || true
+      wait "$server_pid" 2>/dev/null || true
+    fi
+  }
+
+  trap cleanup EXIT INT TERM
+
+  info "Starting FastAPI server..."
+  (
+    cd "$SCRIPT_DIR/server"
+    ./start.sh start
+  ) &
+  server_pid=$!
+
+  wait_for_server() {
+    local base_url="http://${SERVER_HOST:-127.0.0.1}:${SERVER_PORT:-8000}${API_V1_PREFIX:-/api/v1}/bootstrap"
+    local attempt=1
+    local max_attempts="$SERVER_STARTUP_TIMEOUT"
+
+    if ! command -v curl >/dev/null 2>&1; then
+      warn "curl not found, skipping backend readiness check."
+      return 0
+    fi
+
+    info "Waiting for FastAPI bootstrap endpoint..."
+
+    while [ "$attempt" -le "$max_attempts" ]; do
+      if ! kill -0 "$server_pid" 2>/dev/null; then
+        wait "$server_pid" 2>/dev/null || true
+        error "FastAPI process exited before becoming ready. Run ./server/start.sh start directly to inspect the backend error."
+      fi
+
+      if curl --silent --fail "$base_url" >/dev/null 2>&1; then
+        info "FastAPI bootstrap endpoint is ready."
+        return 0
+      fi
+
+      if [ $((attempt % 15)) -eq 0 ]; then
+        warn "FastAPI is still starting. First run may take longer while .venv and dependencies are prepared."
+      fi
+
+      sleep 1
+      attempt=$((attempt + 1))
+    done
+
+    error "FastAPI did not become ready within ${SERVER_STARTUP_TIMEOUT}s: $base_url"
+  }
+
+  wait_for_server
+
+  info "Starting web frontend..."
+  cd "$SCRIPT_DIR/web"
+  ./start.sh start
+}
+
+case "$MODE" in
+  web)
+    start_web
+    ;;
+  server)
+    start_server
+    ;;
+  all)
+    if [ "$SETUP_COMPLETED" = "true" ]; then
+      start_all
+    else
+      start_setup_web
+    fi
+    ;;
+  *)
+    error "Unknown mode: $MODE. Use one of: web, server, all"
+    ;;
+esac