“How does a woman get "wet" without orgasming?”
“Getting wet” for a woman is something like having pre-ejaculate (or pre-cum if you wish) for a man - and for much the same purpose.
The reason for both women and men to exude this moisture if to lubricate the pertinent reproductive organs to prepare for easier and more pleasant penetration.
Women often get a noticeable clitoral/labial erection too which is similar to a male’s erection. It’s just less noticeable because an erect clitoris is much smaller than an erect penis while the fully engorged labia are much like a man’s scrotum tightening up before sex - and the reasons for both are to protect the more delicate tissues from some of the roughness of mating activities.
But, just like a man can get an erection and pre-ejaculation without orgasming, so too can a woman get clitoral erection and “wetness” without orgasming. In both men and women the ‘wetness/erection’ and orgasming are independent of each other.
As both men and women get older orgasming can happen without wetness/erection in both genders which is why there’s a market for intimate lubricants.