It’s not even birtherism though, that context of that was Obama being an illegitimate president as a non-American.
Trump isn’t claiming she’s not an American citizen by birth, he’s just deciding her racially identity for her.
The purpose of birtherism was to "otherize" the candidate, not to realistically expect them to admit they weren't born in the US. The same othering is happening here with Harris. The underlying message to voters being "she's not really one of us".