Cannot register some IDN domains

[yukimorifumi]

I tried to register my Emoji IDN domain (xn–w28h3a7g08jhd.tk) with Cloudflare.

We were unable to identify xn--w28h3a7g08jhd.tk as a registered domain. Please ensure you are providing the root domain and not any subdomains (e.g., example.com, not subdomain.example.com)

What is the problem?
Are emoji domains currently unavailable for registration?

postscript
After further verification, we have confirmed that the same problem occurs with IDN domains that contain symbols other than the pictograms below

xn----h-2za980a2ab8fya4988eia.ml (χ∩--τhιšιδ∩.ml)

[sdayman]

They work:

Maybe it’s this:

Community Tip - Fixing Code: 1049 example.com is not a registered domain

Error Try the suggestions in this Community Tip to help you fix Code: 1049. Background A Code: 1049 is returned when trying to add a domain to Cloudflare. When this happens, in your browser you’ll see the message similar to "example.com is not a registered domain (Code: 1049)". The error Code: 1049 means the domain isn’t registered, the domain has no name servers, the domain name servers can’t be resolved, or the domain name servers don’t contain any DNS records and as a result the domain can…

[yukimorifumi]

Indeed, your domain and one of my (emoji-containing) IDN domains are working correctly.
However, the following domains still do not work correctly.
What could be the cause?

xn----h-2za980a2ab8fya4988eia.ml (http://χ∩--τhιšιδ∩.ml)
xn--w28h3a7g08jhd.tk (🤔😡🙄🤪😒.tk)

In addition, the DNS authority server is currently not Cloudflare, but it does not work correctly even if the setting is changed.

[sdayman]

You’d have to check with Support to see what’s different.

To contact Cloudflare Customer Support, login & go to https://dash.cloudflare.com/?account=support and select get more help. If you receive an automatic response that does not help you, please reply and indicate you need more help.