Foundation for a 3x3m pergola

Yes, with a roof proper foundations. The suction forces that pull on it during a small storm are incredible. Axel at the beginning of the year tore down our pavilion and only had gusts up to 79 km/h. That is actually nothing.

The thing weighs almost 200kg, the slats open during a storm, do you still think it will fly away?

I wouldn't risk it. Do you always remember to open the slats (which then provide lateral resistance)? A ship weighs several tons and is perfectly moved by the wind. There is a reason why you are supposed to reef the sails in too much wind.

the thing weighs almost 200kg, when the slats open in a storm, do you really think it will still fly away?

3x3m is 9sqm. If that stands perpendicular to the wind, you already have enough wind pressure from wind force 7. Even if it is protected and facing the main wind direction... thunderstorms often bring wind force 8, and near buildings you also have to reckon with wind shadow effects, etc. You can make the pad foundations in one day's work.

Assembly went well, now only two screws have broken off. 10 cm screws, plugged in. Does something like this usually hold, or should the screw be removed? Unfortunately, I can't reach it that way, it broke about 2-3 cm below the surface.

Assembly went well

Or

now only two screws have broken off.

At least you now have a predetermined breaking point and during storms the foundations stay in place.

How many screws are there? 2 out of 4? 2 out of 16?

two out of 12.

The anchors are fully in, the screws are 3/4 in the anchor. Father-in-law says "that holds" :D, I have more doubts, I'm always safety first.