Hey there, I am going to run 6 stepper motors (17HS10-0704S to be specific) from 6 TMC2209 stepper drivers (running at 24V). They will be connected in parallel.

I was hoping to be able to power these 6 motors along with a Raspberry Pi Zero W (at 5V so 24v-5v step down converter) from a LRS-100-24 Meanwell power supply (108W, 24V, 4.5A).

From my calculations, the 6 motors will draw about 60W (2.9V x (0.7A x 2) = 4.06W + some headroom for inefficiency = 10W) which is 2.5A drawn from the power supply. On top of that, the Raspberry Pi foundation recommends 1.2A to power the pi zero w although I doubt it will run at that current continuously (see this). Along with that, I will be running a few neopixels so maybe another +0.3A. Finally, I will be running a small Noctua fan for cooling (+0.05A). This all adds up to about 4A. That being said I am not planning on running the motors at max current, maybe only about half (so 0.35A/phase) so this calculation is only for the worst-case scenario.

My problem is I don't have enough space in my enclosure to use a bigger power supply so I am stuck with the form factor of these Meanwell supplies or smaller. Would the power supply mentioned above be sufficient for this?

I would go fore a 10 Amp power supply. 6 motors * 0.7 Amp = 4.2 Amp. Adding current for the processor might cause that power supply to shut down.
Don't bother soo much about Watt. Current is the important factor.

You've got a point.
Reducing the current to that level will cripple the steppers a lot, reducing the torque they can provide.
Make a test running one motor, setting different currents and see what happens! Choose the most heavily loaded stepper!

No, that is wrong. The wattage is the important factor. The current driver ( TMC2209 ) works similar to a buck converter. Therefore, the current drawn from the supply is less than the motor current. However, a sufficiently large bulk capacitor near the TMC2209 is very important. The full motor current flows between the bulk capacitor and the motor (in both directions!).

So I tried out one motor, and I am able to get it to work for my application very well at around 0.3A (current measured from my bench power supply). With this, I guess the calculation then would be: 6*0.3A = 1.8A, correct?

Those motors are about 2W stationary, lets say upto 4W dynamic. six lots is thus 24W.

Allow for driver inefficiency, 2A at 24V is plenty I think. [ seems to agree with measurements! ]

You calculation is incorrect, a 0.7A 4.2 ohm motor takes I-squared-R, not twice that, since the coils are driven in quadrature. When one coil has 0.7A the other has 0A.

If you use a buck converter to power the Pi Zero, it won't be pulling anything like 1A from 24V.