The effect of measurement reliability on sample size

The following calculator (like many of its kind) uses a number of variables to determine an adequate (and importantly, representative) sample size:
https://www.calculator.net/sample-size-calculator.html

This calculator does not however consider the reliability (or precision) of each measurement taken.

And so by definition it would spit out the same sample size whether I was investigating the country of birth of a sample of people or my guess at their weight. These are clearly two examples exaggerating two ends of the spectrum from 'can measure with factual accuracy' and 'is likely to be hit and miss but hopefully about right' but I wanted to make my point clear.

My question is this. Does the position on this spectrum affect the sample size required? If not, why?

In my head (happy to be corrected), it seems as if a sample size subject to such unreliability would require a larger sample size (unless of course reliability and sample size are two separate things i.e. reliability cannot be improved with an increasing sample).

Note: Apologies if I have confused precision/reliability - I understand they are often taken to mean two different things.

Thank you in advance.