To add, this is of course not limited to Pushkin, it's simply happened so much in his stories it's made me curious.
While you're waiting for a direct response, this older post by u/chocolatepot is well worth checking out. It covers precisely the things you are enquiring about, and does a great job of explaining the ways in which contemporary writers used such tropes to meet readers' expectations, allowing virtuous female characters to respond appropriately to potentially difficult situations:
Female characters often lose consciousness due to the overwhelming feelings produced by stressful events as an authorial tool to a) keep the heroine from being able to leave the situation or protect herself and b) demonstrate her sensibility (that is, sensitivity to emotion).