I have yet to see signs of "many blacks" caring about how authentic her American blackness is. I doubt most people care that she's not a descendant of American slaves, nor is Obama, who is also only half black.Good point
Also many Blacks also feel Kamala is not authentic American Black, she cant trace her ancestry to slaves. actually she comes from slaves owners
I don't recall any cries from the left on the perceived need for Obama to "lean more into Obama's Muslim heritage."