How quickly is the Earth shrinking?

(Related to answers to the question Thermal expansion of Earth, which I only realized after having saved this answer. So, in principle, a double post, but I was asked to undelete :-))

Earth's thermal history may give some hints -- not sure if this is an actual answer to the question. It seems like Earth's radius depends on the layering of mantle convection, and that though there were significant changes during the Archean Eon and earlier, the current and recent (since the late Archean) shrinking rate is slow (a reduction of 12km in radius in 2.5Gy).

Source: Expanding-contracting Earth by Tsuchiya et al. 2013 in Geoscience Frontiers

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Questions that remain:

What about the core ?

And is mass loss or gain from astronomical processes significant enough ?

I would like to add that WGS 84 is a reference ellipsoid, and height values can be (are) given as positive or negative numbers. They can be updated every now and then by satellite. Also, I would assume that tectonic processes or local anomalies may by far outweigh any signal from thermal shrinking over the course of next centuries or even millennia (speculation).