The problem was that it looked like it was going to install the whole of GSX again. Nothing suggests that it installs the updater program in my case
In fact, it's exactly the opposite: nothing in the installer suggest you can install an FSX/P3D product. The only indication you can get from the installer about installing an FSX/P3D Product is a Message Box telling you can't an FSX/P3D products, because those have their installers available otherwise, and the it stops there because there's just no code in the Universal installer to install GSX.
If you assumed it was installing the whole GSX again, it wasn't installing it, it was updating it, likely because you haven't updated in a while, so the update downloaded many files, but it was still an update.
Even then running it came up with a Couati scripting error message that required ignoring to continue
If with "running it", you are still meaning the Installer, the only possible message about Couatl could be an alert from the installer saying you were trying to run the installer while couatl was still running, that's the one and only message about it in the installer.