Every single time an update comes out, GSX makes a complete mess on my system. See attached screenshot.
Your screenshot clearly prove the problem doesn't have anything to do with GSX, and it's caused by a problem on your local cloudflare node, because it's saying the latest version is 3.6.6, when version 3.6.6 is nowhere to be found on our server, we only have 3.6.8
If your local cloudflare node is serving you wrong/outdated files, you can expect nothing will work correctly, because if even the version number is wrong, who know what else might be outdated.
When you suspect the problem might be related to network (and that version is clearly a tell-tale of that), the first thing to do is trying the Offline installer, linked in the Sticky thread of this forum.
However, the Offline installer is not complete, it will only give you the latest GSX code, not models/objects/textures, so it would be best if you fix your network issue and run the normal update online. This might be solved using a VPN software, which will connect you to another node of another country, I suggest something in Western Europe or the US.