Stage started at 34:52.42 (that's the first frame it fades out of black) and Stage ended at 37:38.68 (first frame you can see the "Perfect" sign popping up)

37:38.68 - 34:52.42 = 2:46.260 or 2m 46s 260ms

Got this stage on my recent WR but I'm almost positive I've had faster while practicing but regardless this is a really good starting point at least. You can even see the time to save but this will be a super annoying stage to grind if it gets to that point lol.