Custom domain routing to Flask server with custom domain always showing in address bar
I managed to solve it by myself, but I'll add this as an answer since evidently someone thought it was a worthwhile question.
It turns out that it was just me that did not understand how DNS works and what the difference between DNS and domain forwarding is. At most domain hosts you can configure "domain forwarding", which sounds what precisely what you need but is NOT. Rather, for the simple usecase above, I went into the DNS Zone Records in the options and created a DNS Zone Record type A that pointed xyz.com to a.b.c.d. The change does not seem to have propagated entirely yet, but already on some devices I can see it working exactly how I want it to, so I will consider this issue resolved.