Me and several people had thoughts about why gawain could have run away, but after her revelation I'm sure most are wrong, it can't be low self esteem and fear of socializing, she definitely didn't pass that vibe, it can't be fear either of not knowing which side to choose between Arthur or 4KOTA, she didn't seem undecided, my biggest bet is that there's just no reason, she did what she wanted lol, Tristan left and she did what she wanted, went out to explore the city , has nothing behind his escape and was probably just a spontaneous part of his personality, not unlike when Gowther would just freak out and do random things for Liones.