The last weeks I ran into many problems with CRS in QGIS. The behaviour seems completely weird to me and it is hard to reproduce the problems / bugs. There is a chance of getting completely different results even if I follow the exact same steps. I use QGIS 3.14.0 but had similiar problems with QGIS 3.10.6 or 3.10.7 with PROJ 6.3.2 GDAL and OGR 3.0.4
But anyway, I give it a try:
I downloaded osm-data from quickosm plugin into my QGIS Project, which is a virtual layer in EPSG 4326. It is projected correctly in East Germany. The project CRS is 25832. I export the layer (save features as) into a geopackage layer and choose EPSG 25833 (not 25832) as coordinate system (zone 33 instead of zone 32). When I add the exported 25833 layer to my 25832 qgis project (or another project) the data is shown near the equator and not in East Germany where it should be. But when I export the virtual 4326 layer to EPSG 4326 or EPSG 25832 it is shown in the right place.
This is already strange, but when I change the project coordinate system from 25832 to 25833, the 4326 and 25833 layers are incorrectly projected near the equator. This time, the 25832 layer is correctly projected.