My current setup for this:
I own a domain - say homelab.com - and use it exclusively in my internal network.
The public DNS records do only resolve to 127.0.0.1 (as my domain holster doesn’t want me to have no A record).
In my home network I have a pihole running that resolves this domain and it’s subdomains locally (say pihole.homelab.com, proxmox.homelab.com and so on).
For HTTPs: As this server is not publicly reachable, I use the DNS API of my domain host to get a let’s encrypt certificate with the DNS-01 challenge. That way, the internal systems do not need to be exposed to the internet.
Edit: Caddy can do DNS-01, but you usually have to compile it yourself to include the plugin for your provider. To circumvent that, I’m just using plain old certbot and told Caddy to use the certs that are already on the machine