Pi-hole not blocking ads with Asus RT-AX88U

Ok then:
If your dhcpcd.conf is still looking as posted by you above, and your Pi-hole machine is connected via Ethernet (eth0), then you can switch off your router's DHCP server and enable it on your Pi-hole via Settings | DHCP.

Note that your clients will only request a new DHCP lease from Pi-hole once their existing DHCP lease (as issued by your router) is about to expire.
You can wait this out or force a DHCP lease renewal for a client by dis- and reconnecting it to your network, e.g. by switching WLAN on and off or by power-cycling a device.

Once they acquire their lease through Pi-hole, they will use Pi-hole as their sole local DNS server, and they'll also show up under DHCP leases in Pi-hole.

Do not turn on Conditional Forwarding - you risk closing a DNS loop otherwise, as your router is still configured to use Pi-hole as upstream in its WAN settings, and you don't need it anyway, as Pi-hole knows your client names via DHCP now.

You can use the same diagnostic nslookups as used before:

nslookup pi.hole

That should return Pi-hole's IP.

nslookup flurry.com

That should return 0.0.0.0.

If you have a WiFi laptop, use that to verify.

If you are just using Smartphones via WLAN, you may not be able to extract that information on device. Some models may reveal the DNS servers somewhere in their WLAN or device info settings, some won't. Using a terminal app doesn't help: Even if they support nslookup, they often use a set of static DNS servers instead of the system provided ones.

Your choice of upstream DNS would depend on your personal preferences.

If you are worried about third-party eaves-dropping, you may opt for DoH or DoT.
While this is an area of concern for nomadic devices (e.g. a laptop in a public WLAN cafe), this is hardly an issue when at home, and you should also be aware that any DoH or DoT DNS service provider would still have your complete personal DNS history in any case.

If you are concerned about privacy, consider unbound instead:
DNS queries are resolved recursively starting with the root servers, so no single DNS server will ever have your full DNS history.