Cloudflare supports NS records, which is what you’re looking for. Except it probably only lets you create a zone for the top level domain, so you can only delegate to other providers. AWS Route53 will let you create subdomain zones, and will let you create NS records to set up delegation.
Departing a bit from other advice. Have fun however you think that’s possible. If you choose to get emotionally involved, you’re bound to get your feelings hurt. But don’t worry about hurting either of them.