Earlier quoted context omitted.
They are completely independent protocols, with their own issues in this area. For the DNS, the specification for DNS over TLS is almost trivial. DNS over HTTPS is a bit more tricky because their are more possibilities, interactions with HTTPS, etc. But still not very hard from a protocol point of view. Operationally, DNS over TLS/HTTPS is mostly unknown. So it will take quite a bit of time before it is well know how…
They cannot be independent if actual privacy is concerned. At least sharing a threat model that touches both layers.
For TLS, the threat model is relatively simple: only an on path attacker has access to a plaintext SNI. In the context of route hijacks, 'on path' is not as simple as it sounds, but route hijacks are relatively rare.
For DNS the situation is much more complex. You have to consider not only traffic between stub resolver and recursive resolver, but also between recursive resolver and the various auth. resolvers.
At the end of the day, you need to consider all places where information is leaked and whether you want to do something about that or not. And in that sense DNS is independent from TLS.