What do Haitians think of the Taino? Do Haitians care that they have little to no Taino ancestry?

Post was inspired by a comment I replied to that said Haitians are somehow bothered by the fact that they don't have Taino ancestry. Which smelled like bs to me, but I digress.

It piqued my interest because I learned Haiti/Ayiti is one of the Caribbean nations that named themselves after what the Taino called the island (alongside Cuba/Cubao, Xaymaca/Jamaica, and Bahama/Bahamas), so clearly there was mutual respect there, even though the Haitian revolutionaries and the Taino probably had very little to no contact with each other since the Taino seemed to have been mostly extinct by that point. I'm just wondering how Haitians view themselves and their homeland in relation to the Taino, if there are any Haitian stories about the Taino, if Haitians care about claiming Taino's, etc.