I want to make a kinetic sculpture of the JWST using a Stewart Platrorm for each mirror. I imagine I'll use linear actuators or servos. Power distribution seems fine, the only thing I have no idea how to tackle is controlling that many devices. Is there some sort of multiplexer that would be good in this situation? Or specific micro controllers? I assume I'll need each of the actuators connected to PWM pins. What would be my best option?
you need an HBridge to control a linear actuator - depending on the power you need may be something like the BTS7960 if you need high current
some actuators have a builtin feedback potentiometer so you can know the current position
some tutorials (hope your advertising filter is on, this site has advertising all over the place but it was the first google hit - I'm sure you can find others)
the L298N from this tutorial is not super efficient, Pololu has lots of choices that are better (and more expensive)
Servos can be controlled with 16-device boards such as the PCA9685 based ones that are common on the internet. Something like this:

They have configurable addresses, so many can be placed on the I2C bus of, for example, an Uno. 108 could be managed with 7 such boards.
There are further details to be refined, such as power, distance from controller, etc. but that's the fundamentals.
First thing to do is determine what you really need. Maybe someone here is familiar with what you're describing, I'm not.
You can multiplex on or off but PWM and servos can't be multiplexed. You'd need individual PWM drivers with their own PWM generators (once you've exceeded the PWM pins on the microcontroller) or individual servo drivers.
Length and amount of wiring becomes an issue. If each actuator requires 3 wires to control, that needs over 300 conductors to route to a central point. TTL signals used in SPI and I2C don't travel well off board, especially if you have a lot of motors around creating noise.
A typical way to implement the solution is to have several controllers, for example one controller for each mirror. This limits the wiring needed between controller and actuators. Local controllers would be connected by a network designed for robust comms, e.g. RS485, Ethernet etc, and power connection.
A central controller would issue commands to local controllers and provide synchronization.