The answer is, she’s not. It was a gift from her “father” intended to go along with her new shipsuit on the recon mission to scout out the uptime ship. Like her gloves and boots, it’s red(dish), and as Ari said, it’s all about the accessories.
The unit patch on it is not a unit patch; while it’s shaped like one, it has a Lion Rampant on it. She’s not military, so it’s de facto not a military beret – or wasn’t, when she first wore it. Besides that, it’s not solely a “parachutist” beret to begin with – try Googling “maroon beret us military”.
However, in the years after the Lion of God mission, the Marines of the 1/1 Space Force Marines sought and were granted authorization to wear the maroon beret, with the Lion Rampant unit patch, as a symbol of that first major spaceborne mission (other than the removal of the RIFs to Sanddoom, which didn’t count), for which they were also awarded a unit citation. The 1/1 SFM are therefore known as “The Lions Rampant”, or sometimes more familiarly, and only among themselves, “Ari’s Own”. (They were previously known as the “Infidels”, but decided they liked “The Lions Rampant” better. Wouldn’t you? Besides, Ariela is much easier on the eyes than some stinking, flea-infested muj.)
Task Group One, consisting of the six US Space Force frigates under Commodore LaForrest, were included in the same unit citation, but did not petition to wear the beret.
The only civilian authorized to wear the maroon beret with Lion Rampant unit patch is Dr. Ariela Rivers Wolff, M.D., Ph.D. (TL1). The only USSF Marine Reservists authorized to wear the beret are MAJ John C. Wolff, Sr., USSFMR, and MAJ Christopher L. von Barronov, USSFMR.
Space Force Corpsmen embedded with US Space Force Marines units are also authorized to wear the beret during their time with the unit. (They’re medical people, after all, and any greenhorn private objecting to a corpsman wearing the beret is simply answered with, “Ari would approve,” and his squad leader takes the next opportunity to impart to him the Legend of the Lion of God.)