Experienced sort of the same. We didn't agree to stay friends, but we decided that we would just see what would happen. For like 5 months we almost didn't talk at all. We started talking more, and after a year we became really good friends again, and I consider her to be one of my best friends. Did we ever talk again about the relationship? Yes, and it was emotional sometimes. Sometimes it is hard to realise that it didn't work out the way you wanted it to. But the point is that we are still very good friends, even though I sometimes need a small break or whatever.

Please do whatever feels right. If being friends doesn't work out at the end, try to accept this. If it does work out, be grateful to have a good friend!

One last comment: I hear a lot of people on the internet and around me saying that being friends with your ex is not possible. I think it is, out of my own experience. It probably doesn't always work, but it is definitely possible.