good Q! i’ve only ever used rich black in black graphics that i bring in but not worried about it for photos…
There are conversations in adobe community about it but frankly i do not understand color profiles and seems they are not very conclusive either! i’ll post them here just in case you have patience and understanding! I’d be interested to know if there’s a quick answer to your Q!
https://community.adobe.com/t5/photoshop-ecosystem-discussions/rich-black-in-color-photos/td-p/13704145
https://community.adobe.com/t5/indesign-discussions/problem-for-achieving-rich-blacks-with-images-photos-for-printing-delivery/td-p/10775224
https://community.adobe.com/t5/photoshop-ecosystem-discussions/i-want-to-change-the-composition-of-black/m-p/10848030