Romance stories do tend to romanticize stalking aka "secretly following to protect", although I've never read one where they follow the person all the time without even an introduction like in this one. The Ml from Not so sidekick occasionally magically spied to see what funny antics the Fl was up to, then he blatantly gave her a gps doll when she was being chased by very persistent bandits. But that doesn't count cause she agrees to be tracked?
The Ml in Wrong House Villain stalks the Fl half out of curiosity and half for protection, but she tells him stop it's not cute when she finds out. Idk if he does, that's the latest chapter.
Another western novel had the ML regularly break into the Fl's apartment to 'check if she was still alive', the Fl brushes off his actions as 'werecat things', but is suspicious cause he also ate the pie in the fridge....
But in all my examples, and in most of the other stories I've read with 'protection stalking', the Ml and Fl are at least at the flirting around stage. Never basically strangers like here.