Was in a new Civic with new driver and he was at very low speed and braked to the car to get out. Was stopped or slow enough that passengers had doors open, but maybe it was not actually at full stop (though it felt like it was) and car made a short clicking noise going into Park. How much damage, if any, is that likely to cause if it was slightly moving or is this possibly something else? Hondas tend to be engineered pretty well and can't image that the something should fail from that happening unless it is a regular occurrence or really bad metallurgy. Maybe the prawl is scuffed,but should not be broken. Interweb is all over the place, but most comments seem to be that everything should be fine and to just not do it again. Others predict doom and gloom.
Stop overthinking!

if the park gear still holds the car, then what's the problem?
You don't want to tear out the whole transmission do you?
First CVT. Park gear seems to hold fine. Placed car in Park (without parking brake) and gave a nudge from front and nudge from rear -- being careful not to push too hard on body and car does not roll away. Seems to resist adequately enough -- no different than the other car. Brand new car -- not going to attempt to have somebody tear the car apart "just in case" but looking for warning signs, other advice, or confirmation that life will go on just fine.
You just tested the warning signs. Life is fine 🙂
But nothing in life is certain.
How much damage, if any, is that likely to cause if it was slightly moving or is this possibly something else?
Probably nothing.
I accidentally shifted into park in the past and it was ok.