Ok something is going on: On my test system (software stack is the same as on my production system, one Windows Server 1016 has been cloned to the test system to be able to analyze this issue) I updated the system to the latest version with (upgrade / dist-upgrade, now PVE 5.1.36) and then I downloaded the newest virtIO drivers (0.1.141) because I stumbled upon this bug report:
https://bugzilla.redhat.com/show_bug.cgi?id=1451978
The bug report is for a different version (not the 1.126 which is still marked as stable) but since the issue sounds related and I don't have anything to loose, I gave it a try. I updated all virtIO drivers and services (netKVM, virtio-scsi, Balloon drivers and Service, Guest Agent ...) and did a reboot. Guess what? Problem gone!
I did a ping test while doing a backup of the machine and a complete DB check at the same time and when I did this before I was kicked out of my RDP session for minutes and had huge package loss and delays. Now: Not a single glitch. I can use the browser to scroll web pages under heavy load and no single packet loss (ping max was 0.3 mSec).
I did a few more checks on my test system and after 2 days I decided to do the same updates to my production system with 2 VMs. The issue completely disappeared. In order to be able to switch from IDE to SCSI I had to create an additional small (32 GB) disk and attach it to my SCSI bus so that the RedHat VirtIO SCSI controller was active and I could install the needed drivers. After a shutdown I removed the small disk and changed my drives from IDE to SCSI and started the machine again. That worked well.
I'm still not sure if the latest PVE upgrade, the newer "testing" virtIO Drivers or a combination of both brought the cure.
However, I'm really happy that it is finally working with virtIO-SCSI since the boot times and initial application startup times are much lower compared to IDE for obvious reasons.