I also don't connect PS4 — but if you have your DHCP server issue your PiHole's address for DNS, then you can probably block that ad server specifically (just like you could for Roku/Vizio).
Wondering when the TV manufacturers begin requiring an internet connection to u se, perhaps even hard-coding DNS-via-https addresses.
I don't have to do anything extra. I have a pihole on my network blocking ads, I have a Roku TV that has the ability built-in to stream from streaming services. I connect the TV to Wifi and my goal of having a streaming TV without ads littering the interface was achieved.
Perhaps you stream content to it locally?
I have both a PiHole and SmartTVs — the latter never even get WiFi access (just use them as displays for CCTV & PS4).