Hi Paul,
I installed Photoshop Elements 2025 on my Sequoia Mac and tested your workflow. The jpegs Saved from Elements did not have any Tag, Ratings or Color labels. It seems the latest Elements does not save any of the Photo Mechanic tags in the XMP metadata section. The Rating is an xmp tag but Elements only saves the Capture, Modification and Metadata dates with the xmp tag. I know the older versions of Elements used to save these metadata tags but I'm not sure when Adobe dropped the support.
** Update **
After I installed the Camera Raw plugin for Elements, all of Photo Mechanic's metadata, including the Tag, Star rating and Color label, are imported and saved in a new jpeg. I hope this helps.
Best regards,
--Bob