See when a macOS application accesses the clipboard? On iOS, it now shows you when an app accesses the clipboard. I discovered my weather app is snooping on my clipboard, which is very interesting, especially since I never pasted, and there's no logical reason why it would have needed to view the clipboard:

I very much appreciate this feature on iOS because it creates the right incentives for apps to view only what they have to.
Is there any way to enable this feature on macOS, where a small popup could appear if an application views what's on your clipboard?
There is no way to enable notification of clipboard access with macOS.  This is a system feature introduced for iOS 14. See this UIPasteboard documentation which includes a note about iOS 14 as well as the developer level API for using the clipboard.
If you would like this feature extended to macOS, give Apple some Feedback. I could imagine that Apple might be reluctant to add this feature to macOS because so many apps could be accessing the pasteboard that the number of notifications might be overwhelming.
I can't even see a way of using system logging (via for example the Console App) to detect clipboard reads.  If someone can point the way please add a comment.
Beyond that read @bmike's reply to this question How to secure macOS's clipboard?  Apart from the implementation of the iOS feature the only significant change in the intervening 4 years is the Universal Clipboard which shares the clipboard across your devices.