Thank you for your reply.
I do have a window in focus where the text should be pasted (I tried with textedit, notes, etc), and it works perfectly on my other Mac (MacBook Pro, same OS, same apps installed).
In fact, after the initial beep, the app is still in focus (TextEdit or Notes's menu bar) and each cmd-v will produce a beep (but no paste). Also, at this point, hiting any key (like backspace) also produces a beep with no effect on the text window.
Switching to a background app and pasting in it (or switching back to the initial app