On Pro and Agency you can serve a status page from your own address, such as status.example.com.

• Add a CNAME record for status.example.com pointing to the address shown on the page settings.
• Or add the TXT record _pulsewatch.status.example.com with the verification code shown.
• Press Verify domain.

HTTPS for your custom domain is set up by the site owner (see the owner documentation). Until then the page may only work over HTTP or through Cloudflare's proxy.