I did a quick live stream to try and find a temporary solution to this issue. We did come up with a few steps in the end.
Jump to 56 mins to see the first attempt. But I will summarise the steps below:
Do a hard reset in your console ( hold the power button for 10 seconds).
Try and sign back in. If no joy try and restart the console again and hopefully will be signed in. Keep trying.
Once signed in then don’t sign out and keep trying various games until they work.