While low-altitude wireless networks (LAWNs) based on uncrewed aerial vehicles (UAVs) offer high mobility, flexibility, and coverage for urban communications, they face severe signal attenuation in dense environments due to obstructions. To address this critical issue, we consider introducing collaborative beamforming (CB) of UAVs and omnidirectional reconfigurable beamforming (ORB) of simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) to enhance the signal quality and directionality. On this basis, we formulate a joint rate and energy optimization problem (JREOP) to maximize the transmission rate of the overall system, while minimizing the energy consumption of the UAV swarm. Due to the non-convex and NP-hard nature of JREOP, we propose a heterogeneous multi-agent collaborative dynamic (HMCD) optimization framework, which has two core components. The first component is a simulated annealing (SA)-based STAR-RIS control method, which dynamically optimizes reflection and transmission coefficients to enhance signal propagation. The second component is an improved multi-agent deep reinforcement learning (MADRL) control method, which incorporates a self-attention evaluation mechanism to capture interactions between UAVs and an adaptive velocity transition mechanism to enhance training stability. Simulation results demonstrate that HMCD outperforms various baselines in terms of convergence speed, average transmission rate, and energy consumption. Further analysis reveals that the average transmission rate of the overall system scales positively with both UAV count and STAR-RIS element numbers.