Setting the pi-hole as your DNS server in your router would not work? TV should then use this DNS server after getting an IP-address via DHCP.
The Pi-hole isn't hosted on my local network, but on my Tailscale network because it's running on a VPS. My router can't run Tailscale, so that's not possible.
What router do you have? You'd be surprised, I have tailscale running on a 4-year old Linksys router.