Google Sites does not give option to set Custom Domain

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Sharing for help due to the non-www and www working with Google Sites proxied in my case, I’ve also got 404 in one moment and step, but managed it at the end to get it working - still works via https://cftest.webmaster.com.hr/:

Blogger website issue after nameserver update

If you’re using your full domain name as example.com and also want www, you should consider adding and using only CNAME setup. My domain example.com is registered via 3rd-party domain registrar and actively using Cloudflare nameservers. Nevertheless, when you add your custom domain or sub-domain, you’d get a pop-up message like below: We were unable to verify our authority for that domain. On the domain registrar’s website, find the Domain Name System (DNS) settings and enter the following …