I made a sphere, applied a mountain SOP to it, and then a scatter SOP with 300k points.
When I click “Render As points” and render in “Preview” mode, they are 1 size, when I unclick “Preview” mode, mantra renders them in a larger size.

I tried putting width / pscale as a attribute on the points but it didn't have any effect.

Why are the points renderd larger in “none”-preview mode ? and how can I control their size ?

very easy use a copy node with some @primitive@ spheres on it
and you can control the size of the point.

be ware if you do it as polygon and add many polys will take more time to cook and to render, you just need basic to appear in the rener.