Whether the DNS service logs or not doesn't really matter that much since your ISP can still log all your DNS requests and create an advertising profile based on them. DNS is both unencrypted and unauthenticated by default, so not only can your ISP see the requests, but they can also modify the responses.
If you want privacy, you really need to use DNS-over-HTTPS or DNS-over-TCP. The easiest way to do that is run AdGuard Home. It runs well on a Raspberry Pi or similar single-board computer. Your devices will still use regular DNS to the AdGuard Home server, but by default it uses DoH for its outbound requests.