IE (but not Edge, not surprisingly...) actually has a built-in feature which was probably specifically designed to target such things: https://i.stack.imgur.com/855az.png Selecting "prompt" will result in this: https://i.stack.imgur.com/jvDUh.png I set it to Prompt for trusted sites, and Disabled for all others.
In this case, what I'd like as a user option is to be able to say "Don't copy via app-specific code", i.e. "don't run the js event to let the page populate the clipboard, instead inspect the selection and if there is a text selection then copy that as plaintext, else copy nothing".
An alternative "prompt when the app tries to subscribe to the copy event" could also work. If I select a shape in an online diagram editor and the app says "can I please put my app-specific markup on the clipboard" then I say yes, because I understand there is now way copy paste works otherwise. And on a page when I have text selected, I can say no, and I get the default plaintext copy.
Some apps have this as 2 different functions for a formatted copy/paste vs. raw text copy paste. If browsers had a "copy text" context menu item that copied the raw selection without invoking the js 'copy' event, that would work too.