Nice game! Going *double-jump*, *transform into spider*, *grab onto wall* was really satisfying. I was comparing the movement mechanics favorably to the NES Ninja Gaiden series while playing. The art and music were both lovely, and it felt nice to be playing.
The "input smoothing" for the spider worked fine for me once I figured it out, but still didn't feel like entirely natural, especially when I needed to go from one floating block to the next; it took a few tries to figure out I needed to stop holding right, then press it again to execute that maneuver. I think having the wall-to-wall maneuver triggered by a different button (maybe space? e.g. let go to grab on) would have helped there, because otherwise the input smoothing did feel useful.
One other minor point is that the hit boxes on the thorns felt just a *tad* large to me. There were several times, particularly on the last stage, where I thought I was landing a jump safely but went splat. For "thorny" sprites with a lot of transparent pixels around the edges, I think it is helpful to shave down the hit box a bit to account for the visual perception that the entity is "smaller" than the actual top-left-most/bottom-right-most pixels might suggest. (The piranha plants in SMB1 are kind of an extreme case of this.)
The game design overall was super clever, and it was clear that this mechanic could be taken far. This was a really impressive game jam entry and I'd be very interested to see it expanded into something bigger, with more souls!