Update: Seems to be fixed on WhatsApp 2.23.35.6.
It's a bug on WhatsApp, seems to affect all platforms, and a fix is on the way (here on webcompat).
Workaround
I found this workaround, using this old trick (also here; this didn't work): set
about:config
→ dom.event.clipboardevents.enabled
to false
.
Copy/paste works fine if the text comes from the chat/site itself.
Side effects
With dom.event.clipboardevents.enabled
turned false
you can paste texts, but you won't be able to do things like paste in Google Docs or paste images, e.g. here:
Working privacy-oriented alternatives
Meanwhile, we could use Brave instead of Chrome. It's also Chromium-based (if works on Chorme, will work on Brave), respect your privacy, and have a lot of nice features. If for some reason you don't like Brave, you could try Ungoogled Chromium.
Also, maybe it is time to move to Telegram or (even better) Signal.