The Pin.PULL_UP settings are now Pin.PULL_DOWN, and not really needed.
Because by default, the controller (button) contacts are normally-closed to ground, thus eliminating the need of a PULL_DOWN resistor. The normally-open side is +5VDC.
There is always a caveat: The above reigns true IF a controller is plugged in. If not, the inputs will "float" in an incalculable state. That would be bad, am I right? (The answer is yes)
The bottom line:
PICO's internal Pin.PULL_DOWN setting will work just fine for unconnected controllers.