I've (F) kind of been in this situation, OP. I think you'll get advice here to move on and shut up and leave her alone, but I'm kinda of the same mind as you that sometimes things work out if they're meant to. I left a 7 year relationship and started to hang around with someone, then got a lot of bad feedback from people in my life because I "shouldn't be ready" and we knew all of the same people. I knew there was some validity in taking a break and spending time with myself and not getting into something right away, so I listened. After hanging around with the new person I had to have this weird sucky conversation, like "it's not you, it's me" and did my own thing. I ended up moving cities and going back to school and all this stuff. I rearranged my whole life to do something fresh because I thought that's what I had to do to "heal." months down the line, accidentally got reconnected with the person I liked, it wasn't intentional but turns out I had moved to where they were living. Slowly started spending time together again. Fats forward and we are married.
Like, life isn't a rom com and this stuff doesn't happen perfectly all the time. I don't even know or necessarily believe if you're supposed to have a conversation saying something sappy like you'll wait for her. But I don't see anything wrong with keeping in touch. Still work on yourself and do your own thing. Be yourself, be natural, you never know what could happen. Maybe leave the ball in her court for a few months and just chat, don't smother her. I didn't keep any contact for almost a year with my guy and randomly one night he had a shit night at work and was casually chatting and checking in, then it was like oh holy shit you work at x and live in y? I was alone in a new city and it was nice to have a friend nearby. Took things slow still.
She might have some influences in her life like I did where she feels and thinks one thing but some are telling her it has to go one way. Maybe she's scared of starting something because someone else put that in her head, we really don't know.
Idk man. I don't think there are rules, we can just be as genuine as possible and see where the path takes us.