The website points at another Cloudflare customer. Not you.
The site’s DNS uses a CNAME to a domain owned by a different Cloudflare account, which is not allowed without setup. Waiting won’t change it. Only the owner can fix this.
Nothing on your side causes this. VPN, cookies and browser do not matter here.
Use a CNAME to the origin instead, or set up Cloudflare for SaaS (custom hostnames).
Cloudflare’s documentation