As the others have mentioned, check that TERM is correctly set (it should be something like eat-truecolor), but also make sure that the terminfo file is there. If you’re on Mac or, I assume, any flavor of BSD, the version that comes with eat won’t work out of the box because Linux and Darwin/BSD compile these files differently.

Just run M-x eat-compile-terminfo and that should get you the proper files for your system. Restart eat and it should work.