Look at reverse proxy instead. While you can do what you’re after with DNS, a bunch of the reverse proxy systems will automatically deal with SSL certificate, and there are even a couple that eliminate essentially all configuration outside of your docker file. Like, add a new docker and it automatically configures appName.domain.tld with SSL assigned. And if you ever decide to expose that address to the Internet, reverse proxy makes that simple and provides some security options as well.

I use Caddy for my reverse proxy running from my OPNsense firewall, but if you want the automation with docker there are better options.

Unbound on my OPNsense firewall. I don’t have advice for you, do you have some specific goals besides just having a DNS?

Regardless of what the remote access test says about it being available, I had to manually port forward to fix this same issue.