After trying to activate iCloud Drive I get the weird screen where nothing can be pressed (see below), iCloud Drive stays not activated. The same repeated on the iPhone and the iPad. Both on version 13.6.1.
Step 3 from Get Started / On your iPhone, iPad, and iPod touch https://support.apple.com/en-us/HT204025
Screen I get:
iPhone SE, iOS 13
Restarting a device -- Restart your iPhone - Apple Support.
Apple support suggested to enable Cloud Drive via icloud.com Pages web version. It worked.
What about signing out of the device and back in?
What is the restart you mean? I don't recall seeing a restart option on iOS devices. It's not a single time I see this problem, it's not the single device this problem is visible on. Over the course of a month or so both devices got updates installed, went out of battery occasionally, were turned off an on manually (by holding power key and sliding on the screen, not just put to sleep/wait mode).
That seems to be the same thing I described. Done multiple times. Did not help.
Nope, did not help
Have you tried restarting the device?
Next step -- Get Support.
Not able to activate Cloud Drive - getting strangely looking form
