You might have some issues getting the answer you're looking for since this is a meta question.

My college texts went with 'slave' rather than 'enslaved people,' but I'm not sure how you're defining 'current.' This was ~5-10 years ago, so it's possible popular terminology has changed since then.

Personal opinion: I believe 'slave' is more appropriate. 'Enslaved people' strikes me as an whitewashed neologism that detracts from how horrible slavery was. It dignifies a situation which does not deserve to be dignified. 'Slave' dehumanizes - which is exactly the point. The use of that word should serve as a reminder of how dehumanizing it is. Stylistically, 'enslaved people' is also awkward and unnecessarily verbose, but that's a more minor qualm.

David William Blight, a highly respected history professor at Yale University and authority on slavery in America, has pushed for using the term 'Slave', stating that it is more historically accurate. If one was writing a fictional slave narrative they would certainly use the term slave because it was common to do so. Just look at Frederick Douglass' Narrative of the Life of Frederick Douglass, an American Slave. I don't think you will find a huge consensus on the issue since it seems to have only come up in the past ten years or so.

I also am not sure I agree with him completely, and I don't think my professors would either. Describing someone as 'a slave' is terribly uninformative. It describes a state of bondage, but does nothing to tell you about the person or their occupation. In fact, it likely conjures up a lot of loaded images. You can be pressed into slavery and enslaved, but simply referring to someone as a slave denies them agency more so than referring to someone as a cook or a woodsman because one would refer to a cook as 'employed' just as one would refer to a person as 'enslaved.' An enslaved person can also be a cook. Slavery is not an occupation, it is a legal status. You could similarly call someone a free-man but we don't except in explicit circumstances to make a point.

In short I think enslaved person can be appropriate, but slave can also be appropriate.

It depends on the context.

Someone was captured and enslaved. They were then sold as a slave. Their entire cultural group in the country was enslaved. The masters were over thrown, and the slaves were freed.

All are forms in how I've seen it in recent textbooks.

In textbooks for American k-12 schools, "enslaved people" is strongly preferred, as "slave" can provoke political push-back. It's still used sometimes in reference to slavery in ancient times, but never/rarely in reference to slavery in the Americas.

Editorially speaking, I think it's an awkward phrase to have to use exclusively, and I'd prefer the freedom to use both terms as appropriate. To me, "enslaved person" is a better term for someone who was once free and has been enslaved, rather than someone who was born into slavery.

*edit - k-12 schools

I use both. I prefer "enslaved" because it is more accurate, but stylistically I will use "slave" on occasion just to change up my verbiage a bit in a piece of writing.

Perhaps I am weird. But I believe words have meaning that may or may not be currently PC. But here, I think context matters.

So if the sentence reads, "Most black people in Alabama in 1859 were X" then slaves is an appropriate word for X.

Edit: but enslaved would also work here

If it reads, "Africans in Alabama in 1859 were X" then "An enslaved people" would be fine for X

If it reads, "My primary source discusses how Tom has been working in the cotton fields for ten years, since I bought him at auction." then I think it is fine to refer to Tom as a slave.