To read the clipboard, website needs explicit permission to do so, no way to go unnoticed.
But they can copy to your clipboard for you, a lot of services use "Click to copy" features. But reading is much harder.
iOS before 14.0 appears to have allowed apps to read clipboard contents without making that clear to users. Now that you get a notification whenever an app reads the clipboard, it has become fairly clear a lot of apps are reading clipboards constantly. For what… we all wonder.