I just want to say that I have the exact same problem and found a much simpler but slow solution.
Like OP I also sent a bunch of messages to a bunch of group.
Every other answer gives the same solution. Reinstall whatsapp.
I then figure something out.
We both have sent multiple messages to multiple groups.
So may be whatsapp is still trying to send those messages and I cannot send any other messages until what I send is there.
Solution? I just sleep. The next day the problem is solved.
No need to reinstall whatsapp.
Just sleep. Put my HP on wifi connection. Just wait. Whatsapp is sending all those messages to thousands of people. Once done. It's done.
Update: The solution is not good enough. Yes eventually it works. But now whatsapp delay my messages again. I do not mass send messages anymore.
It seems that this is either a bug or a feature
Web Whatsapp says
Phone not connected. Make sure your phone has an active internet connection.
Any message sent is delayed. There is a clock
If I try to send messages via phone the message is not sent. It's as if my phone is not connected to internet. It is.