It could be a bug, and a bug report would probably help, but only if you isolate the issue by itself with a minimal project.
Similarly, I can't really answer your other questions from just a screenshot.
Re ready for input from the manual:
Is ready for input
True when a peer is ready to send input to the host. This means On client update has triggered at least once, or is about to trigger. Do not allow players using input prediction to move or act before this condition is true or On client update has triggered: doing so will simply cause an input prediction error since the host is not yet ready to receive input
My understanding is that it is used to sync up client input values and local input prediction.
But it shouldn't have anything to do with messages. I'm not sure why it would break your project in the beta, it works as expected when I tested a minimal project. There is probably something else going on. Again, can't diagnose without seeing the whole thing.