fix(bookings): add request struct validation and fix patch test notice logic

Add validators.Validate.Struct() calls across booking handlers. Fix patch test notice period check to compare against booking start time (not current time) and fix expiry check similarly. Update test to match new error message.

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

backend/handlers/bookings/manage.go

@@ -440,6 +440,10 @@ func AdminCreateBookingForUserHandler(w http.ResponseWriter, r *http.Request) {
 		http.Error(w, "Invalid request", http.StatusBadRequest)
 		return
 	}
+	if err := validators.Validate.Struct(&req); err != nil {
+		http.Error(w, err.Error(), http.StatusBadRequest)
+		return
+	}
 
 	// Extract idempotency key from header
 	idempotencyKey := r.Header.Get("Idempotency-Key")