Hurray, I found another bug with only one hit on Google! 
Thanks RobCannaday for the solution!
Custom Engine 4.26, moved project to a new developer machine. All works fine, except very strange behaviors regarding anything HTTP - but ONLY in the editor. Builds from that machine work flawlessly, too.
After a bit - ok I admit it - lot’s of back and forth eventually I see the hanging UE4 editor processes in the task manager and the bloated logsfiles in Saved directory: “LogHttp: Display: Sleeping for 0.5s to wait for 1 outstanding Http requests.” and so on…
Pretty nasty, because the lines only show up after I closed the editor.
For the poor souls who will hit this bug in a few months or years, welcome to the club!
The solution is simple, just edit \Engine\Source\Runtime\Online\HTTP\Private\HttpThread.cpp:
PRAGMA_DISABLE_OPTIMIZATION
uint32 FHttpThread::Run()
{
…
}
PRAGMA_ENABLE_OPTIMIZATION
Then rebuild & enjoy.
For the record:
Windows 11 Home, Version 22H2, Build 22621.963
Microsoft Visual Studio Community 2019, Version 16.11.20