should I get involved with person that may still hasn't let go of their past and previous situations

I came to like one person. We really seem to see eye to eye to lots of things. They also show major interest in me, asking me for opinion on all kinds of topics and engaging discussions, staying late to talk to me, playing games with me, listening to me, opening about personal stuff to me etc. At first I thought they only show interest as a friend but somehow I came to see them as more than friend and also suspect that they see me as more than friend too. They even said to me "You know why I like you? Because I can always talk to you about all sorts of topics and discuss things." Plus they explicitly said "If I wasn't interested I wouldn't be here, this late at night listening and chatting with you." These sentences could be taken as showing romantical interest/having a crush but also wanting to develop close friendship. They said that they have never been understood so well by anyone except me. They also don't open up at all to people, which came to my surprise since to me, they are almost wearing their heart on their sleeve. The problem is, this person was telling me about the girl they used to like on multiple occasions, how they lost contact, how they reconciled, how much they liked her... Today when I asked them how they were/spent the day, out of no where they mentioned that girl, saying how she reached out to them and how they are happy because of it. They are happy she is doing fine and they wish to be visited by that girl and spend time with her. They even said how they made an in-game design while thinking about her because they cherish memories with her. Truthfully, everytime they mention her I get hurt. But today was special kind of hurt. Because I came to realize that maybe they still feel something romantic towards her. I am afraid they are either stuck in the past/living in the memories or they still potentially wish to be in romantic relationship with her. I still don't know the reason they didn't work out as a couple in the past, but the person I like mentioned that they didn't notice small things that mattered to the girl nor did she notice small things about them. I see this as them not being compatible hence none is perceptive enough to understand the other, which isn't the case with me and that person. According to them, the girl saw them as someone frigid, who doesn't open up and won't let her in, which was also surprising to me hence my experience with them being different. I wouldn't like to stick my nose into their business in any kind of way nor do I wish to be reminded of how great their past was. Maybe I am misreading our and their relationship. Maybe I'm walking on thin ice. Honestly, I don't know and I am too afraid to ask since I know the answer may hurt a lot and end what we have now. I already developed a crush on this person, but I don't want to stick around just to be a side piece or second option for them. Also, I don't intend to be a crying shoulder to the person I have romantic feelings for, while they cry for someone else. I've been there, so from experience I don't think I can be that kind of friend to them. How smart is actually getting involved with people that haven't let go of the past? I dislike living in the past since nostalgia is dirty liar that insists things were better than they seemed. Every moment wasted looking back keeps us from moving forward. Even if this person does see me in romantic way, what if there is actually no space for me in their heart? What if their heart is already filled with previous love. What should I do? Should I turn new page? Should I leave silently? Should I keep fighting for them? Right now, I don't have a clue if getting any closer to them could be in vain. Vain longing that vain longing go.