Correct, container does not work with DoH set, see:
http://forum.mikrotik.com/t/dns-not-working-in-containers-with-dns-over-https-setup-on-router/165011/1
There was a separate bug in the ~7.6 where IPv6 resolution was broken – that may also been the original issue in this thread. Which is different from Alpine with DoH.
Alpine’s native DNS resolver only uses UDP and even ignores fragmented responses if I recall right… but there is not “native” DoH support in Alpine.