After reviewing some recorded footage I have found that in the single frame in which you land, all horizontal movement is lost. This is any landing, not just after you jump.

From what I can tell, jumping (including ink jumps) has the same horizontal movement as running. So it may be preferable to jump at times rather than simply running off things.

For example, the two story house followed by slightly raised ground in the starting village. If you start at the top, you could simply run off it without jumping and then jump up to the raised ground (3 landings). Or you could jump and ink over to the raised ground (1 landing). In this scenario, jumping saves 0.06 seconds.

It's not much, but with all the other unnecessary jumps and other landings we're probably still making, it should add up.

Interesting! Another thing I've found is that when you run into an enemy, you are pushed in the opposite direction you are running rather than "away" from the enemy, so if you hit an enemy, for that split animation you can regain lost momentum by tapping the way it threw you to pass through the enemy quickly. This can help quite a bit with the first level, where the timing on the snail&ladybug combos can be tricky. You will still take damage though so be careful

There seems to be a way around the landing frame, sort of. Here's a video I made.

It seems that you can jump as long as you're in the tile above the ground, even if you're only partially in it. If you look, I was only able to do it when jumping up 3 tiles. This would put the landing near the top of the jump arc. I haven't tested it, but I'm pretty sure there is falling acceleration. Since we can't short hop, any height difference less than 3 tiles will have you falling too fast (at least for me) to press the jump button before landing.

To add onto this, from what i found with jumping into a corner for 30 minutes to see if I could OoB. You need to be at a certain height for squidy to shoot ink. If squidy is too low to shoot ink, it'll trigger a jump. I was able to jump again before hitting the ground on multiple occasions, this is seen heavily in the library stage when inking all the books in 3-1 when you have to climb all the 'steps'.

So on fast fall sections, if you are able to time your ink/jump input before landing you could save the horizontal movement (could be very useful in stage 2-1 and stage 3-2.

This is just from a few hours of playing around with the game and glitch hunting. I've found a few ways to clip into tiles, but nothing game breaking.

The 'Mythical' Library skip is the glitch we really gotta hunt for. We've found that the loading zone after Grimwar boss fight (book) is the same zone as the ooblug town with the bar. If you can find a way to gain additional vertical distance, enough to get up to the top of the library, you can skip that fight entirely, saving minutes in a full run.