Copy/paste shortcuts (Ctrl+X, Ctrl+C, Ctrl+V) do not work in the web inspector. If I select some text and press Ctrl+C, it doesn't get copied. If I press Ctrl+V to paste text into the console, nothing happens. But the context menu entries work fine.
Can confirm on GNOME Web 41.3 Flatpak (WebKitGTK 2.34.2). It makes the experience of debugging on Epiphany quite harder, even more so when looking for Webkit specific issues, when using another browser is simply not an option.
I imagine this might be related to not being able to focus and select properly. Try opening the JS console and pressing CTRL + A, it will select the web page instead of the console content.