Just came up with a solution for PS5. Requires losing access to the full map using the D pad though.
Go to options > controller mapping > map the D pad (main touch pad on controller) to ‘toggle chat’. Do this for each of the ‘common, on foot, gunner’ etc. then go to controller tab > controller schemes and change to ‘custom’ for ‘on foot’ ‘’vehicles’ etc.
when the text chat pops up you then can tap the d pad and it will hide. In bf2042 I found the full map not to be very useful and it’s the only key bind I can afford to use. Hope this helps some folks enjoy the game more!