Timed some loads for digital and physical versions of the game I used Nick's run for physical and zimbo's for digital
https://docs.google.com/spreadsheets/d/13CEF2BQXCMeKnQ2199ivY6D2lnn3_PjD9Uwwj5kVXsI/edit?usp=sharing
It doesn't seem like much, I estimate digital saves about 30-40 seconds
Also I believe there is a speed difference between if you have your game on an SD card or on the console. I know because Nintendo said themselves that the fastest load time is on the Switch’s native memory. So if anyone is planning on doing a story run, then make sure it is on your switch itself (you can change the location by archiving the software and redownloading it without the SD card in (for putting it on the switch), and if you want to put it back on your SD card then do the same but keep your SD card in).
After more testing I've found that some loads are actually different per stage, and some stages Physical loses even more time. My estimate is way off and I think it's more closer to 3 minutes I have not timed anything fully though