I feel the need to post some things that I know from watching a lot of the CBT footage on youtube. I have not been able to play NGS in any capacity myself, but I know all of the following is correct.
To get the skill point from the cocoon, you only have to complete it once. Period. Completing it that first time unlocks a skill point to be spent for all of your classes. (NOT just the class that you were playing when you completed the cocoon.)
Cocoons are NOT just jumping puzzles and platforming. Over half of them are combat tests or offer an option path that bypasses all platforming in favor of combat.
Skill points are less numerous than PSO2 classic. You'll need less than 10 points to max out what is currently every class skill tree. This means Cocoons aren't a large focus of the game. They're more tutorials that you find and do once and then don't return to unless you want to try for a better time/score.