There’s another way to check for CGNAT. Go to one of those sites that tells you your public IP like: https://www.whatismyip.com

Now open a command window and do a traceroute to that address.

tracert www.xxx.yyy.zzz

If the traceroute completes in one hop, you do not have CGNAT. If it’s 2 hops, the first one is your CGNAT address and the 2nd is your shared public IP.

At that budget, you’re going to be hard pressed to find anything newer. That’s not a dealbreaker though. The important thing is that the device is still supported by OpenWRT and receiving updates. I have a TP-Link Archer A7 running OpenWRT set up at my parents’ house and it has been rock solid for several years now. They can be found < $40 refurbished and around $55 new on Amazon.

What’s the make/model of the new router? It’s not unheard of to only have one Ethernet port on a router but it is a little unusual.

Does the router actually run Adguard Home or just fill in Adguard’s DNS servers? If it’s the latter, you won’t get the granular control and logs like you do with AGH.