This might be a known issue already logged to Esri Support, BUG-000154896.
"In ArcGIS Pro 3.0.3, right-clicking a layer created in ArcGIS Pro 2.8 in the Contents pane to export features does not include all of the fields in the attribute table."
I can determine if it's the same problem, by looking at the layer file, which you can generate by right-clicking the layer, select Sharing>Save As Layer File and email the result to dflater@esri.com. The layer file doesn't contain any sensitive data, only the layer property definitions.
You can also try searching for "Copy Rows" in the geoprocessing pane and use that simplified tool to export the output .csv. The problem above relates to the Field Map parameter of the export tools.