Will Arduino Mega support stepper motor NEMA 24, NEMA 34
I'm using 4x Nema 24s for a CNC project of mine.  They only need a couple of signals/pins each from the Arduino to work, the rest is up to the stepper controller board.

For my steppers, I'm using TB6600s, since I need ~3.5 amps per motor/channel.  There are others out there that'll work, but it's what I saw other people at my maker space using.

Nema34s would probably need higher rated amps, so that would determine what controller you need to use.

In fact, every motor is rated for different amps and voltages, so that will always determine what motor controller you use.  Since you need a higher voltage to run the motor controllers than the Arduino, using a separate stepping power supply is a requirement.

The Arduino gets hooked to the step/pulse and direction pins of the motor controller and the other pins on the motor controller go elsewhere.  The CNC motor controller shields you normally see are for lower amp controllers and do most of the pin connections for you.  With the higher amperage motors, you'll have to do this yourself.

When you determine what motor controller you are going to use, find a wiring diagram for it (and maybe a friend) to figure out how it should be wired.