From my understanding they use ECS but in an anonymized way (don't ask me how they actually do this. Too technical for me also). Maybe that's why those test pages do not detect it as it was modified for privacy.
The setting in NextDNS clearly says it does use ECS:
View attachment 292568
Anonymized doesn't mean it's not visible/hidden, it just means that instead of using your exact IP or IP subnet it uses the ASN number of that region or something like that. I don't fully understand ASN number yet, but some details are present in the NextDNS article you gave above, as well as in this AdGuard article.
EDNS Client Subnet is a mechanism used by DNS resolvers to to deliver location-specific results to clients. It's widely popular, but also not without its drawbacks. Are there ways to improve it?
adguard-dns.io
AdGuard took inspiration from NextDNS's approach and made some tweak of their own to further improve cache hit ratio.
My IP address starts with 103 while the ECS that I get from AdGuard starts with 203. Both IP belongs to my country, but they are not the same, hence still private to some extent. So when DNS is queried with the ECS IP subnet, the DNS server still knows that it's coming from my country and serve IPs for/closest to my location if available.
So the ECS shouldn't be hidden to a testing site as far as I understand. No issue while using AdGuard DNS on that site, who is doing almost exactly the same thing as NextDNS.
Besides, NextDNS has their own testing site,
You should see an ECS entry here if ECS is working for you. If you see, then the previous testing site has an issue.
Here's mine. No sign of ECS here.
The nice thing is, you can use this site to test ECS with any DNS provider.
Here's the same site with AdGuard DNS, and there we have ECS. You can test with Google DNS, Quad9 with ECS or anything else.
Another method that is given in the NextDNS article is by using DIG. This method is applicable to NextDNS only.
dig malwaretips.com CHAOS
I already have dig installed on my Windows. You will have to install it for testing. Here from the result we have another confirmation that ECS is not being sent when I am using NextDNS.
So you can try these methods to see it's actually working for you.
ECS not working for many users is a long known issue. It never ever worked for me.