Just don't mash the trigger all the way? You don't have the haptic feedback of such a trigger wall but claiming it's "impossible" is a bit extreme. A nice threshold mapping could arrange for that e.g 0-10% dead zone, 10%-80% main mode, 90%-100% secondary mode, _ factor in rate of press to avoid misfiring main mode. Which is probably the logic that it implements already, except with probably a bit more leeway thanks to the haptic feedback.
"Impossible" would be playing a typical† dual stick game with a gamepad that has none (e.g original PS1 gamepad)
† like a FPS that uses the now classic stick layout for quick yet precise movement + orientation
Honest question as I'm curious and don't have access to a PS5: what about PS5-only games that happen to exist on other platforms that don't have such features? Can they be played with a PS4 controller?
Oh and to be clear: it's not a Xbox vs PS thing, I find them both equally guilty of excessive e-wasting / platform locking, just in different ways.