Actually in real applications, whether to update your actor&critic per step or update them after collecting several episodes does not quite affect the performance of your algorithm.
However, it could be very inefficient to compute backward pass per step, as you cannot fill up your cpu ALU units or CUDA cores on your gpu, the computation price would be way too expensive. Therefore, batching is an economical choice., although it does not conform to the “theoretical model” of the REINFORCE algorithm.