Carbon capture, utilization, and storage (CCUS) can play critical roles in transitioning to global net-zero emissions. However, existing works only focus on small-scale or local CO2 utilization. For the first time, this paper proposes a cooperative planning model of multi-energy system and CCUS considering the regional CO₂ availability. In this model, the multi-energy system and CCUS are coupled through interconnected energy hubs. To leverage its inherent operational dispatchability and flexibility, the physicochemical and thermo-electrochemical processes of CCUS are mathematically formulated with source-sink matching analysis. The multi-energy planning is a demanding optimization challenge owing to its inherent nonconvexities and substantial energy-interest couplings. The original problem is firstly relaxed as mixed integer second-order cone programming (MISOCP) to ensure satisfactory computational efficiency. A carbon-oriented bargaining problem can then be reformulated to share the cooperative surplus, which is further decomposed into a joint investment/operation subproblem and a cost-sharing subproblem. The proposed methodology is benchmarked over interconnected energy hub systems to show its effectiveness and superiority in technical, economic, and environmental aspects.