Apex domains cannot have CNAME records.
Question and response
Question
dig berch.network. NS
Answer
berch.network. 1 NS marjory.ns.cloudflare.com.
berch.network. 1 NS beau.ns.cloudflare.com.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0