On page 266 of the Core Rulebook, there is a contradiction:

In the chapter "Distance", it says under Range 3: "The next row of squares after range 2".
In the Diagram 6-1 on the same page, however, range 3 is 3 squares wide, not one.

I assume the diagram to be correct (range 3 is 3 to 10 meters, which is not well represented by just 1 row).

Indeed.

Honestly, I would have done it as Range 1 is 1 square, range 2 is 2 squares, range 3 is 3 squares, and so on just to make it easier to remember.

Range 3 should definitely be a sizeable chunk of space, as narratively it covers from "I can reach you without moving with a spear" to "effective shuriken and throwing knife range".

That's a lot more than 1 square of distance.

Do not use grid rules.

(This is only a suggestion).