There is no csxs5-PHXS.log there. I have recently deleted everything from my 'Temp' folder, maybe this log didn't recreate itself after that. The cef_debug.log is sent. I tried to uncheck the 'Allow extensions to connect to the Internet' several times, and all the 'App is not Online' entries indicate that.
Ok, after a couple of reinstalls I got the csxs5-PHXS.log in the 'Temp' folder.
The problem is solved. Thank you for the session, Neha!
If anyone gets a problem like this, try emptying the extensions cache (there are several folders, not just the Local/Temp one) before reinstalling your add-on.