FWIW, if you have been signed in, you can still use SketchUp offline, it only needs to call the servers once every 28 days (7 days when in trial)
you’re allowed to install SketchUp on two machines, if you log in on those machines, you shouldn’t log out and back in every time. The information is ‘logged’ in your User Data. When the server is down and you canot use SketchUp, two things can be the case: 28 days period is past and your not able to log in again, the other being that the Userlogs have been erased or not written properly (Read write permissions, not installed by rightclicking on the installer file and choose ‘Run as Administrator’,etc.)
If you wanted to activate a classic license on a machine during the time that the servers went down, you also would not have been able to activate your classic license. (They are hosted on the same servers)
The message: ‘An internal entitlement management service error has occurred’ is different from the messages we receive when the license server is down, btw. This message seems to refer to difficulties with the system that manages the assignments: those who were entitled, do not get access.