I think macOS 11.3 has finally fixed this!

Also experiencing this issue which has drove me insane for the past couple of months. A quick fix for this, albeit not permanent, is to react to any message in the thread (i.e. thumbs up, thumbs down, heart). This will quickly reinstate the input. The only other thing I think might be worth a shot is somehow removing all message history from you Mac, essentially so it's totally clean (as if messages has never been setup) and then resync with iCloud messages. Does anyone know how to do this? Where all the associated files and preferences are located?