Lanscaping and exterior design improvement for new home

I am having a bathroom renovated and you can see a different texture on the wall vs. the area that was spackled. The paint on the spackle is smooth whereas the paint on the wall is textured as expected from the roller. The painter told my PM that this is normal and cannot be fixed without a skim coat. That doesn't make sense to me. The spackle takes primer/additional coats but should ultimately have the same texture. Correct? I've attached a few pics for reference. It's a bit hard to see but it does show the difference.

Currently I'm in the process of prepping to repaint the trim in my kitchen and I need advice. Here are the details. - trim is currently painted with oil based Benjamin Moore Imprevo oil paint that is shiny and smooth ( can't remember if its satin, semi-gloss or gross but definitely looks glossy) - I'm in the process of sanding it - I plan to put a coat of Kilz Original oil based primer over it to be followed with BM Advance semi-gloss water bourne enamel Here is my concern: I've tried sanding the old trim with every grit of sandpaper from 120 to 60. When I rubbed my finger over it the area sanded felt rough. But when I wiped off the sanding dust with a damp sponge the trim looked and felt smooth. So I'm questioning whether I need to sand it more before I prime the trim? Or am I over thinking this and the fine scratches created with the sandpaper despite the apparent smoothness will allow the oil primer to properly adhere? I appreciate and need your input so I do not mess this up Thank you