feat(api): add /health endpoint with Docker healthchecks

Allow Docker to distinguish a running container from one actually
serving traffic by adding a /health endpoint that pings the database.
Returns 200 when healthy, 503 when the DB connection is lost.

Add HEALTHCHECK to Dockerfile and healthcheck config to the server
service in docker-compose.yml. Also add start_period to the existing
db healthcheck for consistency.

server/api/endpoints.go

@@ -1,6 +1,7 @@
 package api
 
 import (
+	"context"
 	"database/sql"
 	"encoding/json"
 	"encoding/xml"
@@ -443,3 +444,30 @@ func (s *APIServer) ScreenShot(w http.ResponseWriter, r *http.Request) {
 
 	writeResult("200")
 }
+
+// Health handles GET /health, returning the server's health status.
+// It pings the database to verify connectivity.
+func (s *APIServer) Health(w http.ResponseWriter, r *http.Request) {
+	w.Header().Set("Content-Type", "application/json")
+	if s.db == nil {
+		w.WriteHeader(http.StatusServiceUnavailable)
+		_ = json.NewEncoder(w).Encode(map[string]string{
+			"status": "unhealthy",
+			"error":  "database not configured",
+		})
+		return
+	}
+	ctx, cancel := context.WithTimeout(r.Context(), 3*time.Second)
+	defer cancel()
+	if err := s.db.PingContext(ctx); err != nil {
+		w.WriteHeader(http.StatusServiceUnavailable)
+		_ = json.NewEncoder(w).Encode(map[string]string{
+			"status": "unhealthy",
+			"error":  err.Error(),
+		})
+		return
+	}
+	_ = json.NewEncoder(w).Encode(map[string]string{
+		"status": "ok",
+	})
+}