Your tests and logs go to prove that Pi-hole's filtering is not causing this issue.
But somehow, Netflix doesn't like talking to a DNS server that is not public, with the router being the only exception (as demonstrated by @JonnyB's router cascade). This is probably due to Netflix seeming to be excruciatingly rigorous at shutting out access via VPN or through a proxy.
Now, I don't have a Netflix account, an Asus Router or an LG TV, so the following paragraphs are kind of a blind shot attempt to apply a mildly related solution to a different problem. You have to decide whether it's worth a try.
When trying to fence my TV from leaving my home network in ways I didn't approve of, I ultimately resorted to putting it into a separate WLAN raised by a separate Zero W where all DNS traffic was forced to Pi-hole, regardless which DNS server my TV was using. To that end, I had to alter the Zero's prerouting table.
As far as I am aware of, Asus routers allow ssh login, so you could give that approach a try by extending your router's iptables. I won't post them, as there is an easier way in your case: You happen to run your router with Merlin, so you can set up DNS Filters.
From the UI, find LAN | DNS Filter, switch "Enable DNS-based Filtering" to ON, and select "Router" from Global Filter Mode. Assuming you have defined Pi-hole as local DNS server via the DHCP settings, leave the custom entries blank.
(I am assuming Merlin's documentation as well as a corresponding screenshot are up to date)
Both approaches - iptables via ssh or DNS filters via UI - should produce the same result:
They force any(*) DNS traffic on your network to reroute through Pi-hole.
So when your TV requests to resolve api-global.netflix.com
through Google's 8.8.8.8
, your router will show that request friendly but firmly to your Pi-hole instead, while your TV thinks it is still talking to Google.
I normally try out my suggestions, but obviously can't do that here - so I can just hope this helps somehow
If you were already aware of those options, it would still be of interest if you could confirm they are not alleviating your problem.
(*): In fact, only the UI option might do that, as there might be other DNS ports (e.g. port 853 for DoT) in use as well that my iptables statements do not account for.