Cooperative transport and manipulation of heavy or bulky payloads by multiple manipulators requires coordinated formation tracking, while simultaneously enforcing strict safety constraints in varying environments with limited communication and real-time computation budgets. This paper presents a distributed control framework that achieves consensus coordination with safety guarantees via hierarchical event-triggered control barrier functions (CBFs). We first develop a consensus-based protocol that relies solely on local neighbor information to enforce both translational and rotational consistency in task space. Building on this coordination layer, we propose a three-level hierarchical event-triggered safety architecture with CBFs, which is integrated with a risk-aware leader selection and smooth switching strategy to reduce online computation. The proposed approach is validated through real-world hardware experiments using two Franka manipulators operating with static obstacles, as well as comprehensive simulations demonstrating scalable multi-arm cooperation with dynamic obstacles. Results demonstrate higher precision cooperation under strict safety constraints, achieving substantially reduced computational cost and communication frequency compared to baseline methods.