KS1 I don't think you're looking at DNS correctly.
DNS is the system that translates URL's into IP addresses so that your device can connect to sites. Computers speak robot, so they understand IP address and not URL's. Humans are not good at remembering IP address, so we use URL's. When you type www.grapheneos.org into a browser search bar the browser "can't understand" (in simple terms) this to connect, it then goes through a 4 step process, changing it into an IP address and then connecting you to the site.
Option 1. If you are using default DNS browser settings (in most browsers) and no custom DNS provider and no VPN then your DNS queries (the translation of URL's into IP addresses) are being handled by your internet service provider.
Option 2. If you are using default DNS browser settings and no custom DNS provider and you ARE using a VPN, then your DNS queries are being handled by the VPN, additionally your traffic is being encrypted by the VPN, and your location is being spoofed. This also means that whatever DNS filters that your VPN provider implements are in effect and are activley filtering things (such as ad blockers, possible malicious sites, trackers, etc).
Option 3. If you are using default DNS browser settings AND a custom DNS provider (like NextDNS) AND a VPN, Then NextDNS is filtering your DNS queries, and the VPN is encrypting your traffic and spoofing your location, but is no longer handleing DNS queries (sometimes these two can conflict, but I have yet to have that issue on GOS). Since NextDNS is now handling the DNS queries, whatever filters you have chosen to add are actively filtering. In addition to this, you can enabling logging and open apps on the phone and see telemetry (connections being made in the background from apps) and block connections that you don't want (usually analytics, that by being blocked will not effect the app from a user perspective). When added to the blocklist, when you open and use the apps in the future they will no longer send off telemetry infomation, this is the biggest perk of using NextDNS is that you can analyze almost all connections leaving the device and block what you don't want.
Changing the DNS in the browser settings will only change who handles the DNS queries, you'll want to keep it on the default setting (which is normally automatic) so that it will use the DNS handler of your system (depending on the option you choose that I listed above). It is not overkill, this is how DNS works.
When things break (sites won't load), there are multiple things you'll have to look at. It could be a blocklist you've chosen to add in your DNS settings, it could be from "over hardening" the browser (putting things such as cookies/fingerprinting settings on strict), HTTPS only settings, if you disabled java script, etc. If you are using brave, the easiest way to test this is by turning shields off and refreshing, if it fixes your issue, then you know it was the browser settings. If it doesn't, turn shields back on and switch your Private DNS to "automatic" (if you're using a VPN, your VPN will be handling DNS queries, if not then it will be your ISP), refresh and if it fixes it then you know it was a blocklist or particular blocked domain you've added. If you do use NextDNS and choose to block app telemetry then know that a domain you add to a blocklist to block telemetry may also break other sites if they happen to need that domain, so you'll have to play around with it.
There is an additional option on some browsers (such as firefox) where you can make the browser use it's own DNS independent from the system DNS, but I believe that to be uncessary and defeating the purpose of using custom DNS. In this scenario your system (apps, etc) would be using the DNS handler of your choosing (your ISP, your VPN, or NextDNS) and the browser would be using it's own DNS handler (firefox for example allows you to use public NextDNS servers for this), but you would be losing all your custom filtering.
I recommend option 3, it seems to be the most hardened (you will rarely if at all get ads), but you will break more shit.
cheers.