This doesnt help my problem. Is there anyone who has another idea, what might be the problem is?
If it doesn't help your problem, it's because you either haven't correctly excluded the folder from the antivirus, or you haven't run the update after doing that, or you haven't reinstalled, which are the 3 things I suggested to check.
You can be sure we DO install Couatl_MSFS.EXE, without it, GSX will never run, and if this really happened, we would have the forum flooded by thousands of reports of the file missing. The most important file of the whole install, that is.
Instead, in the few cases were this ever happened, has all being fixed by acting on the antivirus Exclusion then updating/reinstalling, since the antivirus mistakenly removing it it's the only possible reason why a file that is surely included in the installation, could be missing after installing.
Last thing: is it possible you are in a country where the internet is censored ? If yes, you might need to use a VPN to install.