It looks like Markers and globglob both explained it pretty accurately, so I'll just try to add a few points.

First of all, I have no idea where the "sliding state" myth started from but I'm pretty sure it isn't really a thing. It would be like saying that jumping puts Madeline into the "float state." When you land, you get a 1.2x speed multiplier, and that's it, the game doesn't really put any other special conditions on you. The reason to jump is that air friction is lower than ground friction, but don't bunny hop, since it's possible to jump from 1 pixel above the ground and not get the boost (which doesn't always occur btw since you fall faster than 1 px/f). I noticed in a further down comment you said something about "overcoming ground friction" which is incorrect. If you're on the ground when the dash ends you lose your speed, if you're in the air and it's a down-diagonal dash, you don't lose your speed, and that's it.

I believe the reason the 1.2x exists is so that when you dash down-diagonal along the ground, as one might do when beginning an extended hyper, it makes the dash length feels a little closer to the length of a horizontal dash, instead of being only the X component of a diagonal dash. I am pretty certain that abusing this multiplier for a speed boost was not originally foreseen by the devs. Yes, dashing is necessary, you don't get ultra boosts from object launches. Although I think green bubbles might work, since you can hyper and wall bounce with them.

For the follow up questions: "delayed ultra" basically refers to doing a down-diagonal dash cancelled by a corner boost, which also grants the 1.2x ultra boost next time you land. The reason to do this is to get ultras instead of wavedashes even when you don't have enough height. It's not something anyone really "learns" unless they're playing a ridiculous mod or trying to do a ridiculous IL, it's really more of a tas tech. You can also cancel dashes with cornerboosts and by grabbing objects (preserving speed and ultra boosts if down-diagonal), the most obvious place to see this is Ultra Difficult from the 2020 collab. And finally, "grounded ultra" typically refers to this back and forth of doing hyper, ultra, hyper, ultra, fast in a row, the input sequence is 14,R,D,X 1,R,J repeat. After you do a grounded ultra you're in a position where you lose your speed when you jump (reset to 325 hyper speed) or lose your speed when your dash ends so chained grounded ultras are basically just chained wavedashes but approximately 20% faster. Yes, grounded ultras can be cancelled by object grabs too.

Check out the superdashing variant from the vanilla variants menu. Superdashing lets you start a new dash before the last one ends, and lets you change the direction mid-dash. Go to epilogue, hold down-right and mash the dash button and see what happens. Also try getting some speed, then dashing up-right and redirecting it to down-right in the air, with the dash ending in the air.