I love the artstyle and ambiance of the game, but there's some issues that I think should be addressed.

Movement was a little rough at first but it didn't take a long time to get used to for the most part. Acceleration and deceleration during a run could be a little faster.
Also, you should be able to buffer entering doors with an up-input. I frequently overshot doors I was trying to enter by pressing just a little too early. I think you should be able to enter doors in the ghost house without a lantern to let players challenge themselves.

The armadillo guys I think need to make it clearer when they are about to pop while being held. The timer for that is also quite short I feel compared to SMW. All other enemies weren't too much to write home about, but I did like to see the more unique enemies like the macaque or tanuki ninjas (that should probably also turn to face the player). More level sections that force me to interact with them would be great.

It may be due to it being a demo but the story beats did feel disjointed. I think if you're going to show cutscenes in entirely different places I think there needs to be more context before hand like some kind of establishing shot. Maybe make these cutscenes as in-between blips on the map path? Also scene transitions seem to be a little glitchy. The game is still very cute and I think some extra flair in the cutscenes and maybe punching up the writing a bit would go a very long way.

The boss was not very enjoyable. The restart system is thankfully very forgiving and I did figure out in a couple tries to jump onto the wind-up key (maybe stop it spinning to better emphasize this?). However not taking damage right after getting a hit or stubbing your toe on the corners on the giant boot is a different beast entirely. On-top of how slippery the movement can be it was a test of patience for sure.

Overall the design of the outdoor levels felt very "safe" and could use some more zany designs to make them more memorable. Context specific items, more puzzling platforming, secrets or incentives to explore, ect.

All in all, a solid start and cute as hell. My favorite parts were probably the ghost's tower and the yuri. Inspiration and homages to great games like SMB3 are great, but don't be afraid to inject modern design sensibilities and UX to make the game your own.