The smaller the camera (matrix), the faster the focus, is this usually the case?

Question

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The smaller the camera (matrix), the faster the focus, is this usually the case?

Answer 1

No. Not this way. But close:
The smaller the matrix (sensor) - the greater the depth of field
And this means that the less carefully you need to get into sharpness, anyway, a person will not see the difference.

Answer 2

Since autofocus works due to software implementation, in cheap cameras, due to infrared illumination, the distance is immediately determined, in more expensive ones (DSLRs, semi-DSLRs), the software drives the lens itself back and forth in the search process to catch the maximum contrast.
In principle, both methods are almost equal in time, differ only in quality.
Well, the speed of work laid down by the manufacturer.

Answer 3

Not this way. The size of the matrix does not matter. Focusing is (simplified) contrast and phase.
Contrast focusing takes longer and is less accurate.
Phase - faster and more accurate.
In addition, the speed of focusing can be affected by the speed of the autofocus drive, which, in fact, moves the glass in the lens.