Android added a setting called Private DNS in Android 9 (2018). It uses DNS over TLS for the whole phone. You'll usually find it under Network & internet, though the exact path varies by phone maker. It has three choices.

Off uses the network's plain DNS.
Automatic is the default. The phone upgrades to encryption when the network's resolver supports it.
Private DNS provider hostname sends every lookup to a resolver you name, such as dns.example.

Hostname mode is strict. If the phone can't reach your chosen resolver, Android reports that the network has no internet access instead of quietly using plain DNS. On Android 11 and later, a Google system update lets phones use DNS over HTTPS with a few well-known providers.

iPhones have supported encrypted DNS since iOS 14, with both DoT and DoH. There's no simple switch in Settings. You install a configuration profile or an app from a DNS provider, and it shows up in the VPN and device management area of Settings. Only install profiles from providers you trust, since a profile can change where your traffic goes.