Unreal has something called “spring arm” you can attach to a character:
Does Blender have anything similarly simple?
Some really old Stack Exchange answers allude to a “slow parent” feature, but that was apparently too convenient and has been removed…
I recently watched this tutorial on youtube, where he uses a force field to animate the camera. No idea if that’s what you are looking for but I thought it was pretty clever
I have seen people use a triangular softbody and parented camera for this. Looked good.
Search yt?
Hope that helps