For browsing though, I frequently use iCloud Private Relay, which uses oblivious DNS [2] for name lookups. Cloudflare powers that much of the time too, but at least Apple anonymizes my side of the connection.
[1] At least until ESNI or one of its successors finally become widely supported – then I'll reconsider.
[2] https://www.apple.com/icloud/docs/iCloud_Private_Relay_Overv...
Your router will probably let you specify a pair of IPs for DNS (sometimes it's in the DHCP settings)
Sometimes it can happen that you get a shit resolution, but it's hard to identify if DNS is the issue in home use since there are so many variables.
However, some ISPs have truly terrible DNS service, for example at my father's house, the first request to any not terribly mainstream website (say outside top 1000 most visited or whatever) always misses the first query while the provider goes look it up on whatever upstream they use. In this case it was really a case of using a different DNS provider that doesn't prune the cache so much or that stalls while querying upstream.
Personally I use an experimental DoH service that my employer is working on, and CloudFlare.
"It looks like you're trying to find example.com. Here are the advertisers who paid us to talk to you about example.com" grrrr
It is possible to quickly toggle on-and-off what the configuration profile sets in Settings. I've occasionally had trouble on captive wi-fi portals, like on planes, but I generally remember it's probably the DoH, so I go toggle it off, get connected, and toggle it back on.
Thanks again!