Testing used stock FPS demo code, launched the game in the play in editor, confirmed no issues, paused game, selected the existing/active Player Controller and ticked on ‘Show Mouse Cursor’, then resumed and confirmed it was actively impossible to look around unless the mouse button was constantly held down.
Your comment > This is because when the mouse is visible it is not locked to the game window and only interacting with the game when held.
Makes it sound like this is an issue you are already aware of, though having the axis non-responsive unless a mouse button is held down if the cursor is visible/unlocked is a very strange behavior (and seemingly not documented anywhere public).