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.
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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.)
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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.
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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.