Players can negate all fall damage if stepping up something as they land. This behavior is reliably reproduced and is not random, though getting the correct distance/relative position and orientation between the starting coordinate and the coordinate where the stepping up + landing are meant to happen is vital.

While the landing sound plays after the fall, no damage is taken, and no damage sound is heard (meaning the client hits the ground, but the server does not damage it).

In multiplayer, no falling sound is heard when someone does it next to you. Instead, the landing is smooth (no bobbing up) and slient.

From a discussion in comments, it seems this was introduced at the same time as the fix for MC-153698.

What is not new is situations where the player steps up higher than they are supposed to (image, and stepping up whole blocks in the video). Only the fall damage negation is.

What I expected to happen was...:
...not to step up the block in the video, and to take fall damage.

What actually happened was...:
...I stepped up the block, and took no damage.

Steps to Reproduce:
1. Place a block on flat ground
2. Leave a gap of 3 (air) next to that block
3. Pillar up 8 blocks
4. Walk fairly perpendicularly towards the gap from the pillar, and keep holding the forwards key (no sprinting).

Related but not directly (here, the issue is just the application of fall damage, not the stepping up), is the image which shows a setup where you can start on the slab, sprint jump into the chest (thereby slamming yourself against it), hold forwards, and step up the chest.

Thanks for reading.