Would you include creoles into the AA ethnicity?
Yes, we are Afr'Am. Like I said, there are overarching elements to our culture & heritage that pretty general among African-Americans such as the use of red-rice(Oryza glaberrima) in our meals, use of grounded peanuts(goobers) in meals, the combination of Native-American crops with West African cooking techniques to make AA staple dishes like grits and cornbread.
And on music there's the use of strummed folk instruments like Banjo with has documented and recorded being played by African-American in just about every part of the US and Elongated Minor Pentatonic scales with microtonal bent "blue notes" in our melodies ESPECIALLY with the trade marked raspy voices, as well as off-beat accentuation(nuts and bolts of the backbeat which is also unique to all forms of AA music and not found in other Afro-diasporan music types)
(You certainly wont find anything like that among Haitians or Martiniqueans)
^^^^Much of this has to with the common rice, cattle, cotton culture that the economic landscape of North America demanded on slave industry regardless of it was being administered by French, Spanish, or English unlike in the Caribbean and South America were Sugar & Mining where the bread and butter of the economy. Slavers in French Louisiana are noted in specifically trying to recreated the model of rice plantations of the English/British administered southern atlantic coast upon seeing their success so they could compete. So, as it was be a large number of Upper West Africans slave from the Sudan and Sahel regions were imported into the colonies and much of AA culture, if traced back, to pre-transatlantic era is rooted in the traditions of the Sudan and the Sahel. And if that wasn't enough there was the domestic slave trading once the US republic procured lands formerly under the thumb of European colonialism. The amount of people involved in this movement of slaves was even greater than that of the Transatlantic slave trade. So, no Texas nor Louisiana Africans/AA were ever in isolation from other African/AAs in other parts of the colonial or antebellum US.
And like
@IllmaticDelta said there's also the common influence of the Church traditions as well.
What about descendants of free blacks or descendants of black immigrants that have been here for generations?
"Free blacks", yes. Non-AA immigrants, No.