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For the constellations of the Serpent and Centaur, you can grant skill points to stealth/archery skills instead of "the character can use X." Then, these skill points can still be spent on stealth or archery while moving, but there will also be other bonuses.
So, if the character already knows how to use a skill, then other bonuses are applied. As a rule, these are quite strong modifiers. You can only get +50% speed through the Centaur. Of course, this ignores the small detail that there are few skills for simultaneous running and shooting, and there are no such skills for spellcasting at all.
Of the constellations of the months, I would slightly weaken the Hydra; it's a no-brainer option for a pure combat build. Not only do you simply reduce unnecessary stats, but the percentage bonuses are also through the roof.
Interestingly, I think the Hydra is not very strong. You get a bunch of small modifiers, some of which are not very useful, and others don't seem that significant compared to the character's existing combat stats. The other constellations (except the Thinker) give you 3+ skill points, while the Hydra gives -1 skill point (because it reduces intelligence). If the player doesn't plan to play a stereotypical min-maxing warrior/beastman/chimera with social stats in the deep negative, I don't see much reason to take the Hydra. The Eagle, Whale, Pegasus, Wolf, Narcissus, or even the Altar seem like more useful options, in my opinion.