When setting the Nameserver records to cloudflare, this is not done using the regular DNS WebUI of hetzner. Instead, you have to do this directly where all the domains that are hosted with Hetzner are listed.
You can find the required settings at https://robot.hetzner.com/domain and NOT at https://dns.hetzner.com/
Select your domain and change the Nameserver settings there:
Before:
After:
You can use this DNS verification tool to verify if your records are setup correctly with cloudflare.
You can completely delete the zone for your domain at https://dns.hetzner.com/.