Then I contacted tech support. Three adobe techs in a row for 6 hours were trying to fix the problem. Spoiler: they fixed nothing. They all tried the same sequence of actions and failed multiple times. This looked like madness. Every time they were pointing that it is something wrong with me, not with the app.
The first guy said that it is VPN or firewall. I granted him remote control over my PC. When hi saw that firewall and VPN both were already disabled, he tried to disable them once again. Then he deleted antivirus, removed CC Desktop with Adobe Cleaner Tool and reinstalled it. And it worked for three seconds, then went offline again.
The second guy repeated exactly the same actions with the same result. Then he said that the problem is my admin account, created new admin account and repeated all actions above twice with exactly same results. Then he said that the problem is with my router's firewall. Ok, I disabled my router's firewall. Then tech enabled and disabled router's firewall himself and repeated same actions again with the exactly same result. Then he blaimed my router's software. Ok, I removed router and connected via cable directly.
The third tech saw my message about two previous techs' actions but decided to repeat them exactly the same way ending up with failure again. Then he blaimed my network and provider. After I've mentioned once again that I have a macbook with CC installed within the same network and it works fine he blaimed Windows and told me to write complain to Microsoft.
This is already looking like I am crazy and expecting different result while performing the same set of actions. I've already lost 6 hours, entered my login and password 20+ times and decided not to try my luck with the fouth tech. I assumed that he would produce the same sequence with the same result and end up blaiming fiber optic wire and advicing me to contact fiber optic manufacturer.
I think Adobe ows me at least to resolve the problem and a generous discount next time I'm renewing my subscription.