The one that you can currently export is called an Observation Field. These are user created and are sort of a “wild west” situation, with duplicates and misspellings and abandoned fields, etc.
You can think of Annotations as “official” versions of some very specific observation fields. They are standardized, translated, etc. But they’re unfortunately not downloadable from the Export page (see https://forum.inaturalist.org/t/data-users-what-are-your-use-cases-and-requests-for-exporting-data/2972 and some of the topics linked from it for further information).
If all the observations must already have the Dead annotation, I’m a bit confused why you would want that particular annotation in the export file?