That depends entirely on what capabilities your router has.
Many routers have a setting for the DNS info they give to clients via DHCP, which would mean every client is indeed using PiHole directly for DNS resolution.
Other less capable routers, only have a setting for which upstream DNS server(s) the router should use, which of course isn't going to allow you to do anything with PiHole's group stuff.
But an easy solution is simply to disable the DHCP server on the router, and simply use what is built-in to PiHole. It uses dnsmasq behind the scenes, and as DHCP servers go, it's pretty capable and configurable. This is how I use PiHole on my own network, and have done for years now (with some customised dnsmasq config, because I have strong preferences about my network setup and services).
Most routers do nothing particularly special regarding DHCP anyhow, so no big deal to just turn it off, and use PiHole's stuff.
FWIW, and tangent to these specific points, my upgrade to the new PiHole 6 earlier today was pretty smooth — with the exception of it defaulting to having its dashboard on port 8080 instead of my previous 80. Plus I had to tweak a couple of settings to ensure it loads my custom dnsmasq config. But no deal breakers at all.
DNS doesn't have redirection like HTTP has, so what you describe can only be implemented using port forwarding (or SSH tunnelling, but I've never seen a router with the ability to tunnel DNS in this fashion?).
Port forwarding used like this, won't enable one to use the 'groups' functionality on PiHole — which was the (g)parent thread here — because all requests arriving at the PiHole will come from the same client, i.e. the router. Because port forwarding is more like a proxy than a redirect (to use HTTP terms).
The correct solution here if one wishes to use PiHole's groups — and not have a janky network configuration like you describe here (an extra unnecessary hop for local DNS) — is to either (a) use the router's DHCP settings to tell the clients to use the PiHole IP for their DNS, or (b) disable the router's DHCP and simply use the DHCP that PiHole provides, which is at least as good as what most routers provide (and more configurable than most routers also, should one need to)
Ideally, you do not run DNS on your router at all, and you also block outbound to 0.0.0.0:53 from anything _except_ the Pi-hole, so that there's no convenient way to get to an unblocked DNS by bypassing it.
DNS-over-HTTP is a bit harder to block, and of course malware could have an IP baked in and so bypass this entirely.
I already run OpenWrt on x86 hardware so I have plenty of RAM and disk.
I imagine this is how it’s usually done. There’s no reason to double proxy.
To block Youtube I use:
youtube-ui.l.google.com - exact
youtubei.googleapis.com - exact
(\.|^)googlevideo\.com$ - regex
(\.|^)youtube\.com$ - regex
It's probably overkill but it results in no Youtube until chores are done.