So sometimes Windows 10 claims that there is No Internet when there is.

I don’t know the actual cause yet, and a restart resolves the issue.
(though I do suspect my corporate proxy).

When there is “No Internet” Internet, the Network Connectivity Status Indicator shows a globe.

References:

• NCSI False “no internet” status – Microsoft Q&A
• Windows 7 Network Awareness: How Windows knows it has an internet connection
• Windows shows “Limited Connection” when it isn’t
• Windows NCSI (Network Connectivity Status Indicator) Issue with ZAPP