I could try to update to the hwe drivers if this might help? And I’m already running Ubuntus Kernel 5.0.0 on my 18.04.
However, it’s not clear to me how (outdated) display drivers should interact this way, as - as I wrote - the application itself does not freeze and display update and everything works just fine.
It just does not respond to input events for a (long) while. To incoming messages etc. it responds just fine, displays those immediately and plays it’s notification sounds. I just cannot answer then, until input is accepted again. So if someone writes many messages over a longer amount of time, one after another will appear immediately as soon as they’re sent, I cannot reply to him or her at all. 
Basically a DOS attack then.
In the office I’m using a Thunderbolt 3 dock where my screen, speakers and USB devices are attached, while at home, where I did not noticably observe those input freezes so far, I’m using an USB-C dock (at the same connector) for this. Might this have something to do with the freezes?