Bunny has been around for much longer than CloudFlare. All those third party video streaming websites (e.g. adult content) all rely on CDNs like these. Bandwidth is very cheap. CloudFlare is able to command their prices mostly because of the security features and the fact that they are a pull based CDN. Most of the internet outside of SaaS rely on traditional CDNs like Bunny for low cost distribution.
Did they undergo a rebrand? Did I just miss this company for many years (it's possible)? I'm happy to believe you. But when you say "traditional CDNs," I think Akamai.