It sounds like the chain and freewheel could be full of wax or heavy grease and are deadening the feeling of a chain snapping into place after a shift. Back in the day, people used to soak their chains in molten wax.

I don't know that that's a problem, but you could soak the heavy lubricants out if you really hate it. You would need to ask a shop to pull the freewheel off, then immerse it in a coffee can full of diesel fuel or something.

I would just leave it.