TL;DR: MacOS Catalina 10.15.6 shows a network connection as disconnected in settings while the network is still connected.
Background
I have a few Apple devices solely for research and testing purposes. I do not use them as a daily driver for a few reasons, one of which being a simple distrust of Apple’s business practices. As I was documenting a feature (not a bug) for something else, I noticed a bug (or, maybe a feature, you be the judge) with how MacOS Catalina (10.15.6) informs the user of their network connectivity.
Details
I used to unplug the Ethernet cable from my test Mac Mini to make sure it couldn’t connect to anything. Recently, I have been lazy and simply turned off the network in settings. I did this by making a location called “No Internet” and disabling wired and wireless interfaces. I felt fine with this, because MacOS gave me a very handy stoplight showing the status of each type of network interface. That is, until today.
Today I was writing directions how to do something in Safari and I noticed that Safari loaded the default Apple website as its start page (I have never changed this, as I don’t use it). I thought maybe it was cached, until when I clicked on a link to prove that, it opened. When that happened, the network settings window was open and looked like this: 
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Hopefully you can see why I was puzzled that the Internet worked, since this clearly says that the Ethernet interface is not connected and that my computer does not have an IP address. I decided to check something I trust more and checked ifconfig to see what was up. 
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Clearly, the Ethernet interface en0 is both connected and has an IP! Returning to the network settings window, I noticed that the ‘Apply’ button was active. Upon clicking it, nothing changed on the network settings window, but in the console, it confirmed that en0 was now actually shut down. 
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Obviously, what happened (and happens consistently) is as soon as I change locations to one that has the Ethernet interface disabled, it changes the status of the Ethernet’s icon without actually changing the status until ‘Apply’ is clicked. It also removes the interface information that is displayed and intentionally tells the user that the Ethernet cable is connected, but the computer has no IP address. I figured this would be a consistent issue and not just Apple wanting people to believe they are offline while MacOS can continue talking to Apple, so I tried switching back to a location with Ethernet enabled.
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Not shockingly, the Ethernet status didn’t change back to connected until after I clicked ‘Apply’. So MacOS appears to be in a hurry to let the user believe they are not connected to the Internet, but doesn’t make the same mistake by connecting too quickly. 
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Conclusion
I’d love to chalk this up to just a normal bug, but bugs are generally consistent and this goes right along with iPhones “turn off Wi-Fi” button really meaning “turn off Wi-Fi for a few hours.” I really don’t trust Apple and you should unplug yours if you are trusting the GUI.