I found out if you make a save while sitting on the stool in the japan alley (the one where you pit out food) and load that save when you push the spacebar to get off the stool you go back to the entrance. Right now it just looks like a weird quirky thing but you never know what will be useful later

I did some testing with this with no success so far unfortunately. The stool does transport you back after you do the save/load, but I couldn't replicate this when I did the stool save/load and then tried to warp back to the beginning at a different part of the level. This included inside the lucky cat restaurant, in front of the restaurant, and when you picked up the kidney. I tried other activities to see if they would warp you back like using the payphone, picking up the ramen bowl at the stand by the restaurant, and entering the vase shop. Unfortunately all of those loaded you into the same place.

Also, I don't think the stool warp would save time when heading back to the metro with the kidney (i.e., warping behind the last set of trench coats). The reason is it warps you to the level begin marker by the metro turnstile, so you have to turn around and walk up the stairs to trigger the level to end. So taking that into account it's probably just easier to go through the trench coats the normal way.

There could be other things that I missed but so far it's just a little wonky to be added in the route.