LR 13.2 won't save the current flag to XMP if the field XMP:Pick is missing from the file and no other metadata field has been changed in the catalog. To reproduce:
1. Download and open this tiny catalog:
https://www.dropbox.com/s/1yvu2uib5uup416/pick-bug.2024.03.10.zip?dl=0
2. Select the one photo and do Photo > Set Flag > Flagged. Observe that the pick flag now appears on the thumbnail but Metadata Status is still Up To Date (incorrect)
4. Do Metadata > Save Metadata To File.
5. Run "exiftool -xmp:pick 7.jpg" and observe there's no output (incorrect).
6. Change the caption to "Hello world!". Observe Metadata Status is now Has Been Changed.
7. Do Metadata > Save Metadata To File and observe Metadata Status is now Up To Date.
8. Run "exiftool -xmp:pick 7.jpg" and observe the correct output:
Pick : 1
9. Do Photo > Set Flag > Unflagged and observe Metadata Status is Has Been Changed.
10. Do Metadata > Save Metadata To File and observe Metadata Status is now Up To Date.
11. Run "exiftool -xmp:pick 7.jpg" and observe the correct output:
Pick : 0