I’ve now tried using Fiddle Everywhere to inspect the network traffic. Interestingly, as soon as I turn on the inspection, the requests start going through (and getting the events fired as well) - seemingly because they are now routed through Fiddle. So it does seem like Windows, or UE, is blocking the requests somehow, even when the firewall is completely turned off.
There still seems to be a difference between what I’ve built with UE 4.26 and UE 4.27. In UE 4.26 and lower, no requests are ever blocked. I’m not able to see any big changes to the HTTP module between those versions in the UE source.