Has anyone gotten back together with an ex after you ended it and they moved on to someone else?

My ex and I were together for 3 years. I ended the relationship about 8 months ago, thinking we might be better as friends. The relationship had become toxic at times, and I didn't know how to fix the problems between us.

For the next 2 months, she tried to get back together, and we continued hanging out and sleeping together, but I kept telling her we were just friends, but that I wasn't seeing anyone because I was working on myself. Eventually, she told me she was going to start seeing another guy. That hit me hard, and I realized I didn't actually want to lose her. I apologized, asked if she'd consider couples therapy, and tried to make things work for several weeks, but she said no.

I decided to go no contact and took a 3-month sabbatical to travel. During that time, I reflected a lot on the relationship and realized how much I had contributed to our toxic cycle. I also realized that I genuinely loved her and that she had been my best friend. When I came back, I reached out and we met up in person to talk. I apologized for how I handled things, explained how much I'd reflected on the relationship, and asked if she thought we could try again. The conversation felt a lot like old times, which made it even harder emotionally. She told me she was now in a relationship with the guy she'd started seeing and that we could only be friends.

We texted on and off for a few weeks. At one point I got emotional and again told her how much I'd thought about everything, how much I regretted my actions, and that I'd been working on my attachment issues in therapy. She just wished me well in my next relationship. At the same time, she said she missed me as a hiking/drinking partner and wanted to restart our friendship, even asking if I'd want to go hiking sometime.

I didn't handle that well, so I pulled back again. It's now been about 2 months since we've spoken, but I still miss her a lot. I've barely dated since the breakup and honestly don't feel very interested in dating other people right now. Meanwhile, she seems happy in her new relationship from what she told me when we met, which started fairly soon after our breakup.

I'm trying to figure out what the healthiest thing to do is:

1. If she reaches out again, should I try to be friends while she's in a relationship? Is there a possibility that she still has feelings for me, or would friendship just keep me stuck?
2. Or is it better to stay no contact for now, focus on moving on, and let her relationship run its course without me being involved?

I know I can't sit around waiting for her, but part of me still hopes that with enough time and distance, we might eventually find our way back to each other.