Should the wall be painted first, then roll plaster applied on it?

Hello everyone,
I have a question again. We are currently renovating and want to repaint/plaster the walls.
I tried my luck on an inconspicuous spot and applied a textured paint with a roller. These are prefabricated walls made of drywall or "wooden walls".
We first painted the walls with a white (quartz sand-containing) primer, so the wall was already somewhat white. Now I have applied the textured paint, but quite a bit still shows through, so I probably have to apply the plaster again to get a good finish.
Now my question is, would it make sense to properly paint the walls white first and then go over them with the textured paint? Or does that not work? I have also thought about wallpapering the walls first with a renovation fleece and then painting over it, but I consider the version with painting white beforehand the simpler and faster method.
The fleece of course has the advantage that it smooths out some unevenness, but I would then have to be careful not to see the seams.
Does anyone have a tip? And please no advice like "hire a painting company…"...... we want to do a bit ourselves as it saves a lot of money. The living room will be done by a company, but we want to do an office ourselves. Thanks.

Tip: The textured roller plaster must/can be painted in your desired color! Only textured roller plaster looks like a plastered and unpainted wall.

So you have to paint putty too? I thought you just apply it and that's it? Or did I use the term roller putty incorrectly?

Yep, as long as it is not tinted, every textured plaster has to be painted. Otherwise, it looks sh**ty.

According to Knauf: Easy-Putz can be tinted with the plaster tinting colors Compact Color, so that subsequent painting is not necessary.
==> so tint or paint afterwards

You don't have to paint the textured plaster! You have to apply it properly, then it doesn't look crappy and then (at least in our case) no substrate shows through... so the green in the bathroom is no longer visible after primer and textured plaster.

The colors to dye directly are quite expensive. So we either left the walls white (just plaster, no additional paint) or painted them colored afterwards.