Hmmm ... and just using a big fat randomizing brush ?

An option via the color jitter yeah, but the desired solution should be automated.
I would like a single buttonpress to fill all pixels on a layer with a randomized color.

For clarity, each individual pixel, each with a different randomized colour?

On the assumption of "yes", I recommend you don't use CSP to generate the image.
Here's a tool: https://pinetools.com/random-bitmap-generator
Note that it defaults to 10x10 pixel squares. If you want to randomize every pixel, set that to 1.
Generate an image to your canvas size, then copy and paste it into a new layer.

If you want to generate it in CSP for some reason I could look into that but my CSP is version 1, from before they went to a subscription model. :P

no..but I see how this could have been misunderstood, sorry about that.
For context, this is for the purpose of a clownpass / color ID map.
If you're unfamiliar, imagine having all the pixels in an image that make sense to group (ie: all skin, all metal, all cloth etc) in one stark high contrast color for selection/masking purposes.
I'm no stranger jumping between many programs over the course of a pipeline but doing so for a single action that needs to be done repeatedly would simply be wasteful...as the journal mentioned, part of the desired outcome here was automation, something CSP's auto action could record and replay. So anything that has a higher interaction cost than "1 click" is already too much, really.
Thank you for your suggestion, though!

Ah yes ! I clearly see ! I used this method sometimes.
Sorry for I won't be of any help. Good luck with this.