I'm currently studying coordinate reference systems and using ArcGIS Pro 2.8 to find appropriate CRSs for different circumstances.
To conduct an analysis of land-use change in the EU, would the best CRS be ETRS89 or UTM32? I'm unsure if the analysis would be better thematic or topographic.
ETRS 89 refers to a Geographic Coordinate System, while UTM 32 is a Projected Coordinate System.
I would discard both because UTM only cover approximately 6 degrees of longitude before you start to have visible distortion. Therefore you would need several UTM zones to cover Europe, with complex issues to stitch them. With ETRS 89, a degree of latitude and longitude are quite different at the latitude of Europe (getting worse as you move to the North), so you can't assume that a pixel in the North has the same area as a pixel in the South.
So my recommendation is to use the Lambert Azimuthal Equal Area projection (based on ETRS 89), with EPSG code = 3035 (EPSG:3035). This projection covers the all of Europe, is part of the standard for the INSPIRE directive, and does not distort the area (which is important if you compute statistics of land use).
Perhaps EPSG:25832 is the best for you, as it's both ETRS89 and UTM zone 32N
