For me, she always has to have a set personality and character. She's the most important part of a story to me so she needs to be the most compelling character that embodies the main theme of the story. This requires a personality and for her to show actual emotions and act/react in certain ways (so of course, not just any personality but one that specifically fits this particular story). The romance and relationship with the love interests is also more believable if I can believe that both members of the relationship are fleshed out individuals - that's what allows for a relationship dynamic to exist and for the relationship development to feel natural (so the love interest isn't just falling in love for no reason but in response to the ways the MC acts, which requires her to act in some way at least). Seeing how she is and seeing her act like a real human being means I can love her and understand why the love interests love her too. I just personally think a story is weaker if the main character that we're in the point of view of doesn't have anything at all to them, and barely even reacts like a real person.
In fact, this "no personality" thing is something I don't even think would help with self-inserting that much (just in my opinion), because no one acts like a literal blank slate in real life. Everyone has some sort of personality, so I don't think having an MC that doesn't have one would resonate with anyone that much. You could argue that even MCs that have "no personality" still have one, because lack of a reaction is still technically a reaction (or action) - just one that I don't think many people would relate to (because it's human to react at least in your head and have thoughts, physical reactions, etc), so I don't think it even works as a way to be a universal personality that fits everyone (because most people would probably not react like a blank slate MC - which is basically not reacting at all, I guess). There isn't a single universal way of acting that fits everyone. There are infinite ways to act but the writer cannot just generate infinite actions, even with choices. And choices, which cannot be infinite/unlimited, can't have too much variation either if the writer wants to tell a specific story (which ultimately every story has to be because no one can write infinite stories in one), because the MC will still have to take certain actions for the story to advance and unfold the intended way the writer wants, and act in a way that helps the relationship with the love interests build up in a believable way that feels like it has depth and is emotionally investing for the reader.
If there is still dialogue, some sort of personality is shown through no matter what, even if it sounds "boring," because that's still a way of acting - even if the MC is silent and says nothing, that's still a choice of the MC that does actually show a certain personality/aspect of her character (that she's quiet and doesn't speak much? etc). I don't think it's physically possible for an MC to truly have no personality of her own - unless I guess if you're talking about MCs that have absolutely no inner monologue, no thoughts and no dialogue. But again, not doing/saying anything (or even thinking) is technically still a way of acting, but one that I think most people would not be able to relate to and seems bland to me because there are no thoughts for us to resonate with or identify with (regardless of if we self-insert or not imo).
Actually, I'd like to elaborate on this. It's super long, sorry (as if everything before wasn't long enough...), and only my opinion. In my opinion, stronger characterisation helps with being able to empathise with, and thus better identify with the heroine (as she will seem more human, with many aspects to her that people can relate to, and the more there is to her, the higher the chance for something to be relatable to someone - compared to a blank slate that wouldn't really feel real/human and has nothing much to them, so therefore has nothing that can be relatable imo although others can disagree), which I feel may actually potentially help with self-inserting for some of the people who do it. Showing more of her personhood (feelings, etc) would make her feel more like a realistic person, allowing people to understand her psychology, which I feel would make her more relatable as one would be able to identify with the universal human emotions underneath, and so identify with her more easily overall. Giving her character an emotional journey and character arc that's shown would also imo help emotionally lead us through the story in her perspective and prime us to feel what she does throughout it, which I think would help people be able to feel like her or like they're in her position, helping you see yourself as her if you wish.
Even if she is not the exact same as us, we'll still be able to understand, and thus relate to her thoughts and feelings if the narrative allows her to have them and explains them in detail. And even if her circumstances aren't the same as ours, we can probably still relate to the underlying human feelings behind them. Perhaps a heroine dreams of being a fashion designer. Even if we do not have this dream, we'll probably still be able to relate to the feeling of having a dream or something we really want (to achieve or have). In my opinion, the narrative respecting her as a human being with feelings and hopes and dreams and thoughts, as well as showing and explaining these things in detail, only helps make it more easy to empathise and to see yourself in her (if you want to self-insert). Therefore, I personally think characterisation makes the MC more compelling and helps people resonate with her, and I believe that this could possibly still be the case regardless of how you view her. Either a more compelling independent character, or a more compelling character to self-insert into (and that you want to represent you) because it may make it easier to feel her emotions and see yourself in her and thus as her, possibly. But again, this is only what I believe and I don't claim that this is the case for everyone - I don't want to sound like I'm speaking for everyone because that's definitely not my intention (it's just that I feel like this surprisingly could actually be the case for some people).
In short, I see otome games as narrative-driven games that have the goal of telling a generally set narrative, so, I believe the elements (characters, world, etc) still have to be defined and written a certain way to some extent, in order to go from Point A to Point B (sequence of events to the ending, even if not fully linear) and convey the story/themes the writer wants to tell. And I think the more defined the writer can make it, the stronger they can realise their themes and intended emotions, resulting in a much tighter narrative that is cohesive and emotionally fulfilling. I think as such, I prefer the MC to be well defined to allow for this to happen (for the story to at least be able to be told), and to allow for her character and the story to have more emotional resonance with the reader.