Microsoft has acknowledged a new bug in Windows 10 2004 (May 2020 Update) where for some users the OS is reporting that there is no internet connectivity, despite everything else working as it should.
On Technet Microsoft writes:
NCSI taskbar icon may report “no internet” on Windows 10 2004 devices that DO have internet access
Customers are reporting “no internet” access in the Network Connectivity Status Indicator (NCSI) on Windows 10 2004 devices on devices that in fact can ping internet resources or browse web sites with internet browsers.
Microsoft has known about this issue but haven’t resolved it yet.
It is being investigated by Microsoft currently.
Thankfully, unlike last time when the OS reported this issue, on this occasion it is merely an inconvenience rather than an actual pain.
You can follow the progress of the bug at Technet here.