I want the ML to be a red flag, but not in a way that's irritating to the FL. He might be obsessive and jealous, but FL shouldn't feel suffocated or overly distressed by him. maybe, she tolerates his actions or is completely unaware of them.

kdrama or cdrama or jdrama, etc Everything is fine

(Sorry my English is bad, I had to use Google Translate)

Iyashi no Otonari-san ni wa Himitsu ga Aru - ML is a stalker, FL is unaware of it

Love Better Than Immortality - ML is the villain, FL mostly tolerates/accepts it