When to talk again (mutual decision on parting ways)

Hey everyone, long story short, I’ve met this girl around 2,5 months ago and we instantly connected, we talked a lot when eventually she got weird and a few days later telling me she’s caught feelings for me, I told her I kinda feel the same but she wanted to take things slow. I did a few fuckups by not really giving her the space she asked me for (she has social anxiety) and that seemed to have hurt her a lot. Anyways, after one fuckup on my side things got very weird and we stopped talking for almost 2 weeks, then we did have a talk and she’s told me she thinks she was wrong about her feelings. I told her that’s okay but staying friends probably won’t work out, and wished her a nice life. She then got back to me a few hrs later she agrees with me but said we could try (a friendship) eventually. I never replied to that because imo it didn’t need a reply.

It’s been around a month now since that happened and I think we both had enough time to process the situation, I really do believe her saying she was wrong about her feelings was more of a way for her to get out the situation somewhat easily because of my already mentioned wrong behavior, she was very clingy initially and made me a lot of compliments, overall her behaviour didn’t really need a lot of explanation and really seemed like she was more serious about her feelings.

I kinda wanna talk to her again because I realized my mistakes and think I could do much better this time.

What are you saying, should I reach out again, if yes, when should I do it and how should I initiate the conversation.

Cheers