I don't think the crack is due to impact. It's probably due to the side grazing the pothole. There wasn't damage on the other side. If it's an impact crack, it would likely appear on both sides?
Impact, grazing. All of these common events reduce the life of carbon fiber components. You can consider yourself very lucky that the damage in this case was visible and audible. Carbon fiber components can due to unforeseen loads structurally weaken in an invisible manner, so that the only way you can see the damage is by some method seeing through the material like X-rays. Such an invisibly structurally weakened component can then later suddenly fail "just riding along".
Is this repairable and worth repairing?
In general, cracks should not be repaired, especially on carbon fiber components. A cracked metal frame is perhaps the only exception to this: it may be possible to repair a cracked frame by welding. A cracked metal rim, stem, seatpost, handlebar or any other load bearing component should NOT be repaired.
I would also say that if a wheel has very few spokes like these wheels, if they're repairable you should really consider whether to spend money on such marginal wheels or to replace them with something more durable.
Aluminum rims have a far safer failure mode: well designed rims (rims that have double eyelets and rims that are not hard anodized) bend rather than crack. Such bent rims are always repairable, although if the repair is not done perfectly, you still may have a little bit of tension imbalance in the spokes after repair.
I've read many other posts and the classic answer is "is your face worth more than 1000 dollars for a new wheel". It's of course easy to buy a new wheel, but I'd like a more thorough answer on what caused this crack and whether or not it is still rideable from a scientific perspective.
Fortunately, you need not spend 1000 dollars. I built a new front wheel for my electric road bike by spending 130.57 euros (excluding the tire, tube and brake disc). Due to the current exchange rate, it's slightly more in dollars but nowhere near 1000 dollars. I did not cut corners by reducing the spoke count: there are a total of 36 spokes in the front wheel. If you choose not to build a replacement wheel yourself but pay someone else to build it, it would probably still be below 250 euros.
Usually on wheels if you pay less, you get more (except on maybe the very cheap end). By paying less, you are more likely to have a repairable (i.e. aluminum) rim. You are also more likely to have a wheel having a full complement of spokes (36). Also, Shimano hubs are some of the best bicycle purchases you can make, and they are also some of the cheapest hubs!