Like... It seems creepy because she's being controlling. If what she was acting like a yuri protagonist trying to win someone over, that would be one thing, but she's forcing a relationship on Kurumi, she's repeatedly ignoring and dismissing Kurumi's agency, she's getting possessive over someone she has no right to be, not just in feeling, but also in an attempt to control access to her, she's acting aggressive basically to the point of violence toward others with romantic interest in Kurumi, etc.
A lot of this would be framed as romantic in other works, eg, being jealous shows they love the person, pursuing them is being passionate, being controlling shows they care enough to want to protect the person, etc. I have a hard time thinking you've never seen any romance structured like this, but, for instance, those of who watch anime are getting to see an adaption of I'm in Love with the Villainness where the protagonist is basically sexually harassing the second female lead until she gives in, Bloom into You has a character going along with dating despite not being interested in the person, etc.
(Edit: Also, I think female characters sometimes get away with more in Japanese works because they are seen as more pure and harmless, but I can certainly think of similar romance tropes in male female romance stories like otome isekai stories).
What makes it seem creepy is not the behavior per say (unless you found these other series creepy, which was clearly not the goal of the respective authors), but that we are getting a traumatized MC reacting to it somewhat realistically while we mainly see the story from said MC's perspective. It would be pretty easy to selective edit panels to write from Kokoro's perspective, leaving out various details about Kurumi's background, and then change it so Kurumi becomes interested in her, which would culminate in something closer to a standard romance story.
I may be wrong, but I suspect this trope subversion is intentional from the author. Kokoro is living in this kind of fantasy without stopping to think of Kurumi's actual feelings, whereas Naoi is basically this redpilled character who sees things as they are and therefore doesn't care about following the norms of the various false social realities that surround them. Therefore Naoi must save Kurumi who lives under the yoke of all of the false realities, which is why Naoi has a focus on getting Kurumi to express hidden desires in their interactions while often giving vague instructions.
Another edit: Also re forced seperation, Naoi is not just someone who is interested in Kurumi, but someone who got into a brawl with her and blackmailed her with a cell phone photo. Kokoro is trying to remove Kurumi from a percieved threat, which is in fact common in other works. However quite often it is a real threat in those works, whereas right now in reality Kokoro is like the biggest threat after maybe Kurumi's mother, but even misunderstanding a situation and overreacting in a protective way could be framed as romantic in a different work.