The measurement problem: why everything we measure in science might be wrong

Physics has its famous measurement problem — the observer effect at the quantum scale. But there's a less celebrated version in the rest of science: measurement is always partial, always theory-laden, and always depends on instruments that embody assumptions. The unit of temperature is defined relative to triple-point cells. The length of a meter is defined relative to the speed of light. Every measurement is ultimately circular — defined in terms of itself. At the quantum scale, measurement disturbs the system. At the cosmological scale, we measure distance via redshift, which assumes a cosmological model, which we test via distance measurements. What does it mean for science if every measurement embeds the theory it's trying to test? Is this a paradox, or is it just the nature of knowledge — that we have to start somewhere and that starting point is always provisional? And what would a "measurement-free" science look like — or is that even coherent?