DisplayLink Forum - Display Link Manager stopped working overnight on Catalina 10.15 with MBP late 2013

Hardware:

late 2013 MacBook Pro,
Docking station :Startech.com USB32DP24k6012 connected to MacBook via USB-C cable
2x Dell U2414Hb monitors, each connected to docking station via their own DisplayPort cables

Software:
Catalina10.15.7 (as of today, Saturday)
DisplayLink Manager :

stopped working with 1.4. (Build 57.120)

now installed 1.5.0 (build 58.125) --> still not working

Similar to this thread https://www.displaylink.org/forum/sh...ad.php?p=94959
my device stopped working, but the instructions there did not fix my problem.

Symptoms / Steps taken

Worked normal on friday,the 10.Febr, ran DisplayManagerApp and my two connected screens turned on.

Opened my MacBook today, on saturday, ran DisplayManagerApp, but both my screens stayed black

I unplugged all the cables and put them back in.

I see, that my Mac is trying to share screens, because the display goes from dark to showing its desktop image and turning dark again and so on.
Then I restarted my Mac, and suddenly it says "Mac OS catalina is being installed"

I found out, that a Catalina security update has been installed. I thought it has to do with that, but it got installed AFTER my docking station stopped working.

I did not uninstall the DisplayLinkManager App because I could not find a why how to do it (there was no uninstaller to be found in the zip file "[display link] mac usb display adapter" that I used for my OS Version 15.)

So I downloaded it again and could successfully install it, changing my DP-Manager App Version from 1.4.0 (Built 5.7.120) to 1.5.0 (Built 58.125)

Removed screen recording permissions / closed DL-App / and added screen recording permission again.

No success :(

Should I upgrade to Big Sur?
Sorry for my bad grammar, English is not my mother tongue.

Thanks for any advice!