I'd expect the shower manufacturer to provides some guidelines.
Two attachment points or 8 attachment points ?
What is the Ø of the mounting holes on the shower?

Are there any struts etc behind the aluminum "plate" that the shower could be attached to? Or that a painted plywood panel could be attached to and still maintain the desired mounting location for the shower?

Should corrosion be a concern?

Define "aluminum plate".
1/2" thick ? not much fun with self tapping screws, but if tapped manually 2D thread engagement for 1/4" or M6 fasteners.
Mind the 220 volt cables mounted to the hidden side of the plate.

.018" thick ? Easy for sheet metal screws, but very limited holding power.
Maybe moly bolts or something similar.

Or is the plate thickness in between ?

Sorry I forgot to add. Three bolt holes 3/8” diameter each in an 8 inch diameter circle

Not sure yet on thickness but I assume 1-4” to 1/2” amd there will be a joist or bridging member nearby. 3 total bolts

This was worthy of a thread?

Drill it and bolt it.

I guess my question was the general nature of metal screws. Do I absolutely have to get a nut under there or can the threads hold the equipment in place. It will probably be a quarter inch. Robust enough to walk on

You can locally reinforce the Al plate by welding additional Al plate on top to have enough thickness for cap screws to latch on, provided it is possible under your condition.

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