I wonder what was measuring to that precision with such accuracy! It’s when I think about tolerances on the equipment that’s checking tolerances that I start getting dizzy and retreat to software for a bit.
2.5 micron is basically the metric value for a 'tenth', i.e. one ten-thousandths of an inch. A typical machine shop will usually work in tolerances of a 'thou' or two, but most are equipped to measure to tenths without too much fuss. Standard micrometers have a vernier that reads tenths, and tenths indicators aren't uncommon.
Going beyond that, to tens of millionths or sub-micron, is where things get nutty with special climate controlled rooms. Digital indicators can easily read with such precision, but controlling for factors like radiated body heat become important.
Reference measurement is usually done with gauge blocks and pins. The development and popularization of these sets is basically how mechanical parts became standardized.
If you're interested in that sort of thing - bootstrapping precision and the like - check out "The Foundations of Mechanical Accuracy".
The precision (ability) of the machine rarely matches the precision of the measuring apparatus, if it's even part of the same equipment. And that's usually ok, even preferred, and cheaper.
If it's a rabbit hole you're interested in, then check out the history of geodesy / geodetic surveying & the design of mechanical / optical surveying equipment- especially theodolites & auto-levels (and even chronometers and astronomic observatories, if you want to go 4-dimensional).
It was the "industry" that had a large hand in innovating this technology, which led to the smaller versions used in manufacturing (made even more interesting due to the fact it was all funded to better artillery, and ultimately ballistic missle targeting, sans-GPS.)
I'd be happy to steer you in the right direction, if interested. It's a personal favorite.
Possibly a coordinate measuring machine (CMM) in an environmentally controlled environment, but even then it's coming awfully close to the capability limits
