I used a 10mm masonry bit to drill for a 10mm plastic anchor like that pictured. The anchor spins freely in the hole, which I think is expected. I thought I read somewhere that the screw size should be 2mm less than the anchor. Thus 8mm for a 10mm ø anchor. But an 8mm screw is fat enough to rub sides of the anchor as it is inserted because I suppose the anchor is only 1mm thick at the opening. The guy at the shop confirmed that 8mm is too big. He said a 6mm screw matches and sold me those. After installing and loading, the anchor started to pull out.

Do I need a 7mm ø screw? Odd sizes get decreasingly common above 5mm. Yet 10mm sleeves are very common… so it’s not adding up.

I would like to have a reliable PDF chart of bore,anchor, and screw sizes – in metric. It seems there are plenty of such charts for Imperial/English units, like these:

I’m not sure what a “#10” screw or anchor is (sometimes also written as “№10”). Does that refer to the metric size despite being in an imperial system?

(update)
The brick is rendered over with ~10mm plaster. The anchor is flush with the wall so about 10mm of the anchor is wasted. I think the anchor needs to be pushed in to be flush with the brick. But that’s a struggle. I think the proper approach is to screw in the screw just a couple rotations and then to hammer on the screw. But the anchor is either too big for the hole or something. The screw drives in but the anchor does not go with it. I think I will try softening the anchor with a heat gun and then try to push it in deeper. Or maybe I need a fatter screw just to drive the anchor in more.

The problem is worsened by the fact that as I screw, the anchor is coming out by about 5mm. So it’s even shallower than when I start screwing.

(update 2)
Now I see why I cannot get the anchor to be flush with the brick: I only drilled the hole deep enough for the anchor to be flush with the plaster layer.

So one theory is that I need to drill 10mm deeper so the anchor can be flush with the brick not the (useless) plaster. OTOH, the collar of the ancher seems a bit useless anyway for about 10mm.