Weird. I've never seen this before. I would tend to think that Emacs isn't becoming the key application and therefore you're actually typing into the terminal window. If you select another application, then go back to Emacs does it still type into the terminal or that other application?
Does "emacs -Q" work?
What exactly are you doing here?
Presumably you're running Emacs on a remote, Linux, server, and trying to display it locally using XQuartz over ssh X forwarding?
If so then the locally installed version of Emacs is irrelevant. It's not used in any way. You want to look at the version of Emacs installed on the remote server.
As u/fiddlerwoaroof said, you need to install lucid emacs on the server.
If you just want to run it locally on your Mac then forget about X, install the brew version and it'll Just Work. But it sounds like you already have that working.
I think you can do (sit-for 0) which will force a redisplay, after which, hopefully, your frame will be resized.
Glad you got round it. It's still very weird, though. I wonder if there was some sort of problem specifically with the brew cask build.