It seems unlikely you lose all rights when you die or it would be chaos - imagine all the secrets people die with that affect everyone they know. An integral part of every estate plan would be incinerating records. Wills do have real power.
OTOH, there's a 2004 case, National Archives & Records Administration v. Favish[1], which establishes the surviving family's right of privacy to death scene photos, but that's technically not privacy of the deceased.
[1] https://www.justice.gov/archives/oip/blog/foia-post-2004-sup...