Specifically, you must install a properly configured .mobileprofile with HTTPS/TLS in the DNSSettings > DNSProtocol part of the payload (along with DNS server addresses of course). Merely pointing at a DoH/DoT supporting DNS server in the settings GUI won't do it, the OS doesn't do any probing and automatically use it just because it's available. For applications DNS Settings is covered under the Network Extension framework [0].
It's definitely nice Apple now has this built-in, and since they're onboard with Cloudflare/Fastly maybe this new twist will be pretty fast too. But obviously they're going to have to make this more automated for it to really make a widespread difference, ideally it'd simply see if the supplied DNS server (manual or DHCP) could run DoH/DoT and then just use it by default with no interaction required.
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0: https://developer.apple.com/documentation/networkextension/d...
