When u use your ISP-Modem (should be a router actually) IP as upstream DNS in your NAS, then local DNS and internet-DNS will work with just one entry in your local computer.
I’m also using DNS-Server in my NAS (Synology) but i also have another DNS-Server which is running on a raspberry pi. This is called pi-hole. DNS-Server in my NAS provide DHCP (with some reservations) and is being 2nd DNS. 1st DNS is my pi-hole filtering adsense and local DNS + Internet-DNS.
I’m using also wireguard vpn running on a mango router, so i can use pi-hole filtering and dns also outside my home.