I am having the same exact problem. For the first several days after starting a new character after 2.01 came out, I had no problems. However now whenever I start the game Red Launcher tries to log me in but says I am offline, and if I try to log in or start a new account it says it's not avalible right now. I've tried turning off my entire firewall, clearing my DNS cache, and doing a game files check from Steam and nothing has worked to get me reconnected. Also I truly believe this is a GOG issue because that website wont load properly at all, EXTREME lag and when I do get something to pop in it's some kind of bizzarely corrupted webpage with gigantic text and missing formating.
I should note I am having absolutely no problem whatsoever with any other website or game right now. So someone needs to figure out what the heck is going on with GOG so I can get properly logged into Red Launcher. The problem is also forcing Red Launcher to hang and not shut down when I exit CP2077 which means Steam keeps thinking the game is still running. I have to go into Task Manager and force quit Red Launcher every time right now.