So, having finally finished the original game on 25 June, I eventually started Round 2 over the Christmas holidays, left it dormant for the month of January, and am now on the "Final Duel". The second game definitely resolves a lot of problems I had with the first:

The directional controls are now relative to the camera rather than Kao himself, like a normal 3D platformer. That's a big help for sure!

Checkpoints are now in fixed locations, instead of the player getting a limited number to place wherever they judge best (usually wrong!)

There is now dialogue to explain what's going on in the story

By extension, not every creature you meet is hostile anymore, which definitely makes the world feel more welcoming
It has a few problems of its own:

Dialogue is nice, but the voice acting in the English dub leaves a lot to be desired!

I don't speak Polish, so I didn't bother trying it out in its original language to see if it's any better…

Janky swimming controls in the Ocean World, thank God there were only two levels there…

Too many controls? Maybe it's just me (and/or the fact that I'm trying to pick it up as an adult!), but having "attack", "throw" and "roll" separately gets a bit confusing…
I started playing it around the time of the Rayman 4 leak, and it struck me that the movesets are actually quite similar between the two games! (Double-jump / glide, groundpound, etc.) Thankfully Kao doesn't get stripped naked when he takes damage though!

The ranged combat, with strafing and written sound-effects on each hit, also remind me of Rayman 3, so I see what Rulez was getting at here:
https://raymanpc.com/forum/posts/1220243/