When running the Spatial Join tool, if two fields in the Target Features layer and the Join Features layer have the same name, the output only contains the field from the Target Features layer.
Add new fields with field names that are not identical.Alternatively, ensure there is a unique ID field in the Join Features layer that can be used in the Join Field tool to create another join between the Spatial Join tool output and the Join Features layer. Only select the missing same name fields for the Join Field tool to avoid duplicating other fields.