I do have a higher refresh rate, but even when I set it to 59.951 Hz, it doesn't seem to get much better. I notice the jump height is pretty inconsistent too.
As I'm measuring my jump height in the first pit, on the web version I can jump a little higher. As I said before, I can jump higher than one block at least. Looking at the sprite of the second block, the minimal jump height when I hold for the whole jump reaches the top of the dark part on the second pixel "column", I'd say. I imagine that's about six pixels into the second block? And the maximum seems to be a little over the dark part of the first column, so that should be about nine or ten pixels? Almost enough to jump over the block and out of the pit.
In the downloaded version, I can just barely reach the six pixels, web version minimum as the highest jump height. The minimum is still within the dark part of the sixth and seventh columns, so that would be around three pixels high? The downloaded version also feels like it moves a little slower, but I'm not sure and the audio doesn't sound any different.
Whether or not I hold A or D or an arrow key while jumping doesn't seem to matter. And now I'm testing on 143.856 Hz again, the jumps are also apparently inconsistent there. Though the web version seems to reach the minimum jump height more often, and the downloaded version the maximum jump height, the ranges are still the same. Or maybe I lose one pixel on the web version's maximum?
I don't know if these details matter, but I figured it might be helpful somehow? If not, sorry for the rambling, I suppose. I don't know of anything other than my refresh rate that could affect the game's framerate, but that probably doesn't mean there can't still be something I don't know about on my end that does do something wrong.