Why are data offered in CRS 3857 or 4326 only?

I need to compare Sentinel-2 data of different sources. I noticed a difference in pixel size and orientation due to different coordinate reference systems of the data sources. If I download data directly from the Copernicus Open Access Hub, I get imagery in .jp2 format and EPSG:32633. Data from EO browser is not available in this format or reference system. Reprojecting the 32633 dataset into 4326 or 3587 or vice versa results in same pixel size, but a displacement of 4 meters.
Is there a chance to get data from EO browser in EPSG:32633?

EO Browser does not support this. You can however get these data through the API, e.g.