I'm on PS5 but I assume the options are similar. They're both in the same place - the On-Ice trainer settings, which is found as another box in the main settings menu. Turn both "Shot Aim Targeting" and "Offside Warning" to Off (note: Offside also has an "adaptive" setting which will only pop the red zone up if you have multiple offside situations within minutes of each other).
This menu is where all of the other visual help mechanics are turned on/off - control hints/feedback (the game notifying you that certain mechanics have been triggered - personally I kinda like this one for knowing when a screen has been properly set) the goalie coverage grid, shot lane, pass aim targeting/suggestions (dotted blue line pointing to an open teammate), and defense positioning (only available in player lock, but shows you who you as the locked player are supposed to be guarding and what your zone responsibility is). You may want to consider turning off all of these if you want the "clean screen" experience.