On page
https://exiftool.org/TagNames/XMP.html (https://exiftool.org/TagNames/XMP.html)
I found tag Headline into XMP iptcExt Tags table (This table contains tags defined by the IPTC Extension schema version 1.6...),
but on page https://iptc.org/std/photometadata/specification/IPTC-PhotoMetadata#headline (https://iptc.org/std/photometadata/specification/IPTC-PhotoMetadata#headline)
I found tag Headline into IPTC Core schema 1.3.
You probably need to move this tag to the XMP iptc Core Tags table?
The specification you referenced places this field in XMP-photoshop:Headline. The ExifTool IptcExt tags also contain tags from the IPTC Video Metadata standard version 1.3 (I'll add mention of this in the table description). It is here you will find a definition of the XMP-iptcExt:Headline tag: https://iptc.org/std/videometadatahub/recommendation/IPTC-VideoMetadataHub-props-Rec_1.3.html