What are some eighteenth century anthropological accounts of encounters with Africa?

European accounts of Africa in the 18th century were mostly concerned with the coasts and the areas along the major rivers. Most were written by explorers. They are often called anthropological although anthropology as a distinct social science developed along with sociology in the last quarter of the 19th century.
Regarding European accounts, the British African Association was founded in 1788 by the naturalist Joseph Banks and his associates; they aimed to find Timbuktu and the origin of the Niger. Expeditions with which they were associated increased in the early 19th century.
One very well-known account, a success in its own day, was published at the very end of the 18th century. The Scottish Mungo Park traveled from 1795-1797into the interior from the West Coast, up the Gambia River to the Niger River. His first book was Travels in the Interior Districts of Africa, published in 1799; it is still in print.
Earlier, from northeastern Africa, another Scot had explored Egypt and Ethiopia, reaching the source of the Blue Nile. James Bruce had been the British consul in Algiers beginning in 1763. His Travels to Discover the Source of the Nile (1790) was thought even at the time to have credibility issues.
A Portuguese explorer, Fransisco de Lacerda y Almeida, published a journal describing his travels in the 1790s to Zambia, then the Kazembe-Luanda Kingdom.
The extent to which the explorers understood, or tried to understand, the cultures they encountered remains a subject of debate. As their expeditions were often financed by governments and companies intent on colonizing those areas, their reports were in turn influenced by their patrons interests.
The History and Study of Africa, a very useful overview that includes numerous articles that address aspects of your question, is available online from Oxford University Press.
https://www.dukeupress.edu/travels-in-the-interior-districts-of-africa/?viewby=title.

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