The (wildcard) certs are the same, as it's what caddy is pulling via API. You can either build the cloudflare module into caddy via docker build, or use a prebuilt version. It doesn't create two separate certs for local and remote.

It works really well for me, and is actually the most straight forward way to get valid certs for internal services I've found. Since they're wildcard, my internal domains don't get exposed through certificate authorities.