Hey Markus!
If it does work just fine in safe mode, but not otherwise. This tells us there’s either installed software causing the problem, or a file system issue causing the problem, most likely.
Since, after booting to safe mode and restarting, the problem persists:
I’d first try removing the login items, (Apps set to launch when you login every time), in System Preferences > Users and Groups > Login Items.
Add or remove Login Items:
https://support.apple.com/guide/mac-help/open-items-automatically-when-you-log-in-mh15189/11.0/mac/11.0
Highlight each, (Remember, or wrote down if you need to, them in case you need them to open at login and put them back). Then hit the “-“ sign below to remove, them restart.
If the issue still happens, I’d boot to recovery mode, (Startup your Mac while holding Command R), open Disk Utility from there, select the startup disk, (Under “Internal”), select First Aid, the select Run.
Run First Aid on the startup disk:
https://support.apple.com/en-us/HT210898
Once done, if no errors, restart and test. If the problem persists:
Since it is also related to the network, I may consider creating a new network location in System Preferences, and like the Login Items, remove any VPN type interfaces from System Preferences > Network, in the same way/restart/test:
Use Network Locations on Mac:
https://support.apple.com/en-us/HT202480
I usually remove old kernel extensions, especially ones labeled “Unsigned” or “Unknown”.
Hit the Apple Logo > About This Mac > System Report.
Once there, click Extensions, (Under the software section).
Expand the window wider if you need to.
Once all loads, On the top right, click on “Obtained From” just once, scroll to the bottom of the list.
All the Apple extensions will be in top, the “Identified Developers”, as well as the rest, on the bottom.
Anything titles Unsigned or Unknown, You can click on to find its location below, (Typically now in Finder > Macintosh HD > Library > Extensions).
I’d navigate to those locations and delete the unknown or unsigned kext extensions, (Good to save a copy anyway if you’re not sure), restart and test.
This, I think is a helpful article of other locations to look at for software that maybe causing a problem, especially if they don’t come with or have an uninstalled:
https://www.google.com/amp/s/eclecticlight.co/2016/09/20/my-mac-only-runs-properly-in-safe-mode/amp/
I always do a backup before deleting anything anyhow, always a good idea, but, if unsure Apple is always a phone call away if you need them, best!
