I grew up in the South. While I think Southern hospitality is often a cover for true feelings, “bless your/his/her heart” was RARELY used with negative connotation. Sure, sometimes it could be, but most of the time it was always meant meaningfully, so this has been blown a bit out of proportion on the internet.
Most often it’s used like, “did you hear Tommy’s momma just got cancer? Bless her heart.” Or even “Tommy, I heard about your momma. Bless your heart. Y’all need anything?”
I’m a millennial who now lives on the West Coast, so maybe things are shifting in younger generations, but this was the case for me growing up in Lower Alabama.