In my work I am constantly reading text like "its profile has witnessed a thrilling resurgence recently and is now leading the real estate charge", and so I find "see a resurgence" refreshing literal and uncomplicated.
Going back to the literal root, I suppose it's waves that rise back up. There's not much that literal resurgers can do except resurge; I'd be reluctant to say that a wave literally had a resurgence. So 'have' and 'undergo' are already paddling a little into the metaphorical sea, and 'experience' is only slightly deeper water. What can experience can see. Whatever is personified or reified as having a resurgence has thereby been given other cognitive powers including sight, so they can see their resurgence as they're experiencing it.