As far as I can tell, QGIS has no particular understanding of either a coordinate relative to the (moving!) crust or of a coordinate in space-time that can be projected to space at future or past times. Surely this should be a thing!
I found HTDP, a web tool that can shift coordinates forward and back in time:
https://www.ngs.noaa.gov/TOOLS/Htdp/Htdp.shtml
And I found this discussion:
https://www.gpsworld.com/the-effects-of-tectonic-plate-movem...
But I haven’t found anything easy to use.
(I have an RTK-capable GPS and NTRIP data via UNAVCO from a nearby CORS station. I was hoping that storing position relative to such-and-such CORS station as it was on such—and-such date would be straightforwardly doable in QGIS.)