The steps below are high level, but should provide an outline of how to accomplish what you’re asking for without having to associate your IP address to any domains nor publicly exposing your reverse proxy and the services behind the reverse proxy. I assume since you’re running Proxmox that you already have all necessary hardware and would be capable of completing each of the steps. There are more thorough guides available online for most of the steps if you get stuck on any of them.
Purchase a domain name from a domain name registrar
Use NginxProxyManager, Traefik, or some other reverse proxy that supports automatic certificate renewals and wildcard certificates
Configure both the DNS provider and the reverse proxy to use the wildcard domain challenge
Setup a local DNS server (eg: PiHole, AdGuardHome, Blocky, etc.) and configure your firewall/router to use the DNS server as your DNS resolver
Configure your reverse proxy to serve your services via domains with a subdomain (eg: service1.domain.com, service2.domain.com, etc.) and turn on http (port 80) to https (port 443) redirects as necessary
Configure your DNS server to point your services’ subdomains to the IP address of your reverse proxy
Access to your services from anywhere on your network using the domain name and https when applicable
(Optional) Setup a VPN (eg: OpenVPN, WireGuard, Tailscale, Netbird, etc.) within your network and connect your devices to your VPN whenever you are away from your network so you can still securely access your services remotely without directly exposing any of the services to the internet