Representation for women in gaming just sucks overall. I'm gay and feel like when I can even play a woman, she's almost always straight... You're absolutely right in that there aren't many games with a straight female protagonist that is actively pursuing a man/men, but I really hope you're not trying to imply that the situation is any better for lesbians.
I grew up playing harvest moon (first as the male-only option, then as a straight woman) and it wasn't until stardew valley that I got the option to be gay. I still don't get the option in Story of Seasons. Fire Emblem has had marriage as a system since the 90s, but gay marriage wasn't a thing until fates. Every single woman whose sexuality is known in the tales games (unless I'm missing something from one of the few I haven't played) is straight. In fact, I can't recall ever playing a character who is canonically a lesbian. All the lesbians I've played have been in RPGs where I could also choose to be straight/bi (Mass Effect, Elder Scrolls, Dragon Age). I started The Last of us, but didn't really enjoy it, (and since I barely played it, I'm not even sure if you ever played as ellie in the original).