Spoke wrench conversion master guide
Nipple wrench flat sizes don't correspond to spoke gauge in as clean or universal of a way as you're suggesting.

This depends a little on where you are in the world (and in history), but 2mm aka 14g spokes are by far the most common for bicycles, and there are three different common size nipples associated with them: 0.127", 0.130", and 0.136". (These correspond respectively with the black, green, and red spoke wrenches that several tool companies use.) Of these, the 0.127" wrench flat size is the standard one for 2.0mm spoke nipples by all the modern premium quality spoke makers (DT, Sapim, Wheelsmith, Marwi), and the other two are used seemingly at random by various lower-tier spoke/nipple producers.

Nipples for 1.8mm/15g spokes also almost always have the 0.127" wrench flat size.

2.3mm/13g spoke nipples can have either the 0.136" size or one of the more "oversize" standards like 0.156".

So there is no 1:1 mapping, especially because looking back into history there can be found any number of now-unusual permutations. The gauges listed on ring-type spoke wrenches are arbitrary and outmoded in actual use even if once they were based on some kind of real system.

Also, spoke wrenches in shop use get a lot of reps and do develop slop and eventually wear out.