Hmm. I think the change in DNS Server is a red-herring (which is to say that it fixed the problem only temporarily).
It’s an IPv6-versus-IPv4 issue. For reasons that I don’t totally understand (some combination of my router and my ISP), web requests to IPv6 servers don’t work properly from my home network. They just time out.
nslookup streaming2.qobuz.com
returns both IPv4 and IPv6 addresses. Since getaddrinfo() on Ubuntu is configured to prefer IPv6, Roon tries the IPv6 address(es) first. Only after those attempts time out does it try an IPv4 address (which immediately succeeds).
The solution for me was to edit /etc/gai.conf as described here and reboot.