* are my favorites that I suggest starting with
Thematically similar to what you may be looking for:
Living as the Tyrant’s older sister*
Wish to say farewell
I’m the male lead’s girlfriend
Is it a fortune or is it a woe
Positively Yours
Jishou Akuyaku Reijou na Konyakusha no Kansatsu Kiroku
Namaikizakari
Literally runs at some point:
Sincerely, I became the Duke’s maid*
The Stereotypical Life of a Reincarnated Lady (probably the closest thing to what you’re looking for)
Truthfully, they only remembered her (she’s not running away from the ML in particular but she did leave and is being pursued by all of them)

Does anyone know any shoujo romance manga where the girl runs away or starts to avoid the guy and the guy ends up chasing after her? If anyone could recommend one i would be grateful