Still in love with my ex, but someone new is falling for me. What should I do?

I recently ended a serious relationship with someone I’m still deeply in love with. We didn’t break up because the feelings disappeared. Circumstances took us in different directions and I moved to another country.

I’ve been trying to move forward by building a new life and dating again. I met a girl I genuinely like and really enjoy spending time with. The problem is that she seems to be getting attached very quickly, while I’m realizing I’m probably much less emotionally available than I thought.
Part of me has been enjoying having someone new to focus on. Someone to give affection to, receive affection from, and basically redirect some of the love and attention that used to go toward my ex. I’m increasingly worried that this isn’t fair to her.

We ended up sleeping together recently. Afterwards she fell asleep next to me, while I couldn’t sleep at all. I eventually started crying because I was thinking about my ex and wishing she were there instead. I had to leave the apartment and walk around for a while.

I genuinely like this new girl, so I don’t think I’m consciously using her. But clearly I’m still grieving my previous relationship, and her affection is also filling a huge emotional void.

So I could really use advice on two things:
- What should I do about the girl I’m seeing? Slow things down and be honest about where I am emotionally, or stop seeing her altogether before she gets more attached?
- More generally, how do you actually move on from someone you still love when the relationship didn’t end because the love disappeared? Dating clearly isn’t making those feelings go away.