Scientists measure the speed of light often. Including to test if the speed varies due to some currently unknown mechanisms.
For example, there are varying speed of light cosmological models, and astronomers looking for any evidence that the speed of light was different in the early universe.
I don't know the field at all, so I stuck likely search terms into Google Scholar and easily found papers like https://arxiv.org/pdf/2302.00867.pdf "Do current cosmological observations hint at the speed of light variability?" saying "We find null evidence for the speed of light variability hypothesis for most choices of priors and data-set combinations, except for a mild deviation from it (at ∼ 2σ confidence level) at z > 1 when the a-BAO data are included for some priors and reconstruction kernel cases. Still, we ascribe no statistical significance to this result for the incompleteness of this data set at such higher redshifts."
People also measure the speed of light indirectly, every time someone measures the frequency of a light source, or an index of refraction, or the distance to the Moon (or GPS!), or any of the myriad of measurements connected to the speed of light.
I'll add that my Google Scholar search terms ('"speed of light" early universe measured') pulled up a lot of crackpot-seeming papers, so if you go that route be extra careful.
GPS is all about the difference in arrival times of signals, so it wouldn't make a huge difference if there were a PPB/year difference in the speed of those signals. It likely wouldn't even be noticed by the DOD who runs the constellation.
I think it might prove fruitful to keep on measuring against physical artifacts from time to time. Even a null result can be useful.
In the national metrology laboratories of most developed countries, lengths are measured by interferometry with extremely high precisions, very frequently.
Even very small variations in the speed of light would be detected, because they would cause correlated variations in all measured lengths.
In any case, the point is, as another commenter has already written, that every length measurement done with lasers or radars is a rebranded measurement of the speed of light and such measurements have become very frequent.
The GPS signal includes ephemeris data about where the satellites are located. As Wikipedia puts it, "In addition to the PRN ranging codes, a receiver needs to know the time and position of each active satellite."
Yes, if there's a very small change - and I don't know what the limits are - then it wouldn't be detectable.
FWIW, 1ppm is about 1.2 cm at GPS orbital distances.
My point is still that the speed of light is being measured all the time, not that every measurement is continually improving upon the accuracy of that measurement.
To further complicate things, as far as we can tell the speed of gravity is the speed of light. Should the speed of light change, then either GPS orbits change (due to the change in gravity) or they are not at the same speed.
For example, there are varying speed of light cosmological models, and astronomers looking for any evidence that the speed of light was different in the early universe.
I don't know the field at all, so I stuck likely search terms into Google Scholar and easily found papers like https://arxiv.org/pdf/2302.00867.pdf "Do current cosmological observations hint at the speed of light variability?" saying "We find null evidence for the speed of light variability hypothesis for most choices of priors and data-set combinations, except for a mild deviation from it (at ∼ 2σ confidence level) at z > 1 when the a-BAO data are included for some priors and reconstruction kernel cases. Still, we ascribe no statistical significance to this result for the incompleteness of this data set at such higher redshifts."
People also measure the speed of light indirectly, every time someone measures the frequency of a light source, or an index of refraction, or the distance to the Moon (or GPS!), or any of the myriad of measurements connected to the speed of light.
I'll add that my Google Scholar search terms ('"speed of light" early universe measured') pulled up a lot of crackpot-seeming papers, so if you go that route be extra careful.