How are the numbers chosen if they don't correspond to any actual measurement?
Well, the old law was that density doubled with each node. Indeed, you can see that e.g. from TSMC7 to TSMC5, density roughly doubled, regardless what happened with minimum feature size.
Like the numbers in product names, only with the understanding that smaller is better.
It is an equivalent scale. Density is fine pitchm2 pitchtrack height. You scal node by an equivalent reduction.
It would be better to use logic density, but it is easier to use numbers we are used to.
They divide by sqrt(2) and round to an integer.
https://en.wikichip.org/wiki/5_nm_lithography_process