This is wild speculation, but searching for 'gdal*.dll' in the ArcGIS Pro installation folder, turns up a 'gdal_e.dll' instead of 'gdal203e.dll'. There is no 'gdal203e.dll' in my installation folder. If, like Dan suggests, the GDAL version of Pro is ESRI specific, they may have attempted to rename the DLL to a "version-less" name, but forgotten to update the name in some of the code using it. That would be a bug to report. Other option is that they failed to include this file in the installation, and it is a different one than the 'gdal_e.dll', and both should be on the system.
As an experiment and proof, you might attempt to temporarily rename this DLL to 'gdal203e.dll' as in the error message, although it is likely this will cause many other issues where ESRI did properly change its name in the code base, or if the DLL is a different one than the missing 'gdal203e.dll'.