Assistant (V2): make the 'send' button in the chat gray as long as the llm is still 'typing'

Currently the 'send' button on the chat becomes lit up the moment you've typed anything, but the button can't actually be used yet until it's done chatting.

Either we should be able to already send a new message even though the previous response is still coming in (and have it send when the response is done) OR the button should stay gray until the response is done and then become lit up.