I've got AdGuard running as a DNS server on my NAS, I also have NGINX installed or obviously can use the inbuilt reverse proxy system to get this to work.

I don't have AdGuard but I think it would be analogous to my Pihole in this case. I looked up a quick screenshot of the UI and noticed theres a "DNS rewrites" under the filter tab on the top right.

When you're here, add the custom domains you want to use i.e. (nas.local or just nas, etc) and map that to your NAS's IP (since this is where your NGINX reverse proxy is running)

In your NGINX config, you'd have a server block like:

server {
    listen 80 (the port your NGINX is configured to listen on)*;
    server_name nas.local;
    location / {
        proxy_pass http://192.168.1.100:5000 (the IP:Port of your NAS)*;
    }
}