It may be, however, that the earth’s wobbles month by month and year by year are too slight to be measured.
@m1-6eek-5w1pe, you are right. The perturbations are too small if measured within a certain period of time. So for the long run, it is an iterative process where we will revise the celestial coordinate systems including all the perturbations at certain reference points in time. You might know these points as epochs.
I rather assumed that these changes are measured and recorded.
Yes, they are. And you can compute them for future dates as well. You can find them in an astronomical ephemeris. You can find one at NASA’s Solar System Dynamics website. But this one shows the data you need with J2000.0 as the reference epoch. For your case, you will need a similar calculator but one that uses up-to-date equinox data. Perhaps NASA’s SPICE is what you are looking for. Found a geometry calculator based on the SPICE data as well.