I think a major POD towards ensuring a more interconnected Africa that is more likely to be fertile for a Great Power to arise would be to avoid the breakdown of trade between the Sahel and the Mediterranean due to a religious divide and the threat of piracy. The easiest way to do so without changing too much would be to have a more mercantile Ottoman Empire; IMO the best way to go about doing that would be to have the Ottomans conquer Venice into vassalage; in exchange for access to the Venetian Arsenal and a yearly tribute, the Ottomans could have granted the Venetians equivalent trading rights throughout their realm and protection from piracy. As a result, Northern Italy, the Adriatic, and Venice in particular quickly begin to become the great artery of trade for goods from Muslim Asia and Africa with the Venetians as middlemen, able to trade with the Christians of Europe and in Ottoman ports with minimal restrictions.
Genoa quickly declines in trading importance as the Venetians seize their possessions, establish trade posts and banking houses from Algiers to Basra, from the Crimea to Aden making record profits. In particular, the Venetians are ardent supporters of Ottoman expansion into the Indian Ocean due to a strong commercial rivalry with the Portuguese; as a result it's Venetian sailors that lead the Ottoman charge into the Swahili city states becoming vassals in order to break the Portuguese monopoly in West Africa. The strong commercial rivalry between the two states intensifies over time as a result of their competing area of interest(the Indian Ocean and Africa), goods(ivory, salt, spices), and declining profits due to each state attempting to undercut the other.
On the Spanish seizure of Portugal after the death of Sebastian I, Ottoman reliance on the Venetians intensifies as a combined Berber-Venetian fleet sails for Malta, decisively crushing the Spanish, conquering the islands of Sicily, Malta, and establishing the nominal vassalage of Morocco while in turn seizing the jewel of Portugal's Indian Ocean empire in Goa, but failing to evict them from any of their other Indian Ocean possessions. As a result, trade between India, East Africa, Egypt, and the Mediterranean intensifies in order to compensate for the continued fall of prices as Turko-Venetian and Portuguese ships compete to bring these goods to Europe. The French in particular are eager to encourage competition both to reduce the price of these goods in the noble's courts but to also balance their nominal Ottoman ally for fear that they may encroach on Rome or conquer the Alps, threatening French interests. The Venetians act as the primary provider of goods for Italy, Russia, and Southern Germany while the Portuguese provide for Iberia, England, the Low Countries, and North Sea/Baltic nations.
As a result of the continued rapid expansion of the Ottoman Empire into three different continents, the Venetians begin to struggle to meet their commitments to the Empire both militarily and economically, especially as profits decline over time due to the falling price of goods. It's fortunate that the Sultan at the time, Mehmet III, was sympathetic towards Christians as a result of his Greek Orthodox mother and is well aware of how vital Venetian ships have been in the recent success of the Empire. The crowning achievement of Mehmet III would be his reorganization of the administration; the majority of Ottoman vassals such as the Danubian principalities, Morocco, and Algiers would remain as vassals, but Venice as a state would be made a formal Eyalet administered by a Christian governor, elected by the noble and wealthy families of the Eyalet. Citizens of the Venetian Eyalet would be exempt from Dhimmi taxes, be untouchable by the Janissary conscription system, and would not pay a yearly tribute, being administered instead like a normal province albeit with additional protections for its citizens, regardless if they be in Venice, Zanzibar, or Basra. In exchange for these concessions, the Venetians would establish Arsenals in Constantinople, Alexandria, Salonika, Goa, and surprisingly, Mogadishu due to readily available wood from the Ethiopian highlands. Additionally, the Venetian navy would be formally incorporated into the Ottoman Navy's chain of command, albeit always headed by a Venetian Christian appointed by the Governor of the Venice Eyalet. This branch of the navy in particular would later become popular with the Christians of the entire Empire, as sailors serving under the Venetian arm of of the navy were granted Venetian citizenship for them and their families. The deal was sealed with an agreement between the noble families of Venice and the Sultan to fund the building of a canal in Egypt to connect the Mediterranean and the Red Sea for both commercial and military purposes.
While questionable at the time why such radical steps were taken, it's very simple to understand the reasoning behind these actions; the Ottomans and the Venetians had quickly come to realize over the 50 years since the vassalage of Venice that they needed each other to maximize power and profit. The Venetian navy proved decisive in the expansion of Ottoman power in the Mediterranean and the Indian Ocean, to the point were the majority of the Indian Ocean's Ottoman trade fleet was manned by Venetian sailors. Likewise, the Venetians had come to realize that Ottoman suzerainty led to far more profits than ever before, and the noble houses of Venice were sitting in more wealth than they'd ever controlled. The two entities had had over fifty years to come to terms with their awkward working relationship, and as a result the original capitulation of Venice(the city itself had not been placed under siege for long) was almost looked upon positively by those who had garnered the most gold.
Fast-Forward Another Fifty Years, ~1625-1675
North Africa:
The rise of Venetian trading power in the Western Mediterranean not only saw to the decline of Genoese trade, but also the trade of other European powers save for the Spanish, who eventually limited their trade to a trickle after their decisive defeat to the Turko-Venetian navy. As a result, the Sultanates of North Africa have seen a significant decrease in piracy as its profitability crawled to near nothing, and a shift towards trade and the facilitation of goods from the Sahel. North African cities have quickly become the favored means to transport salt, gold, and ivory from West Africa. While the various Sultanates are not notably prosperous, the region is for a lack of a better term, far more quiet than it's ever been once the threat of Spanish invasion was ended and piracy declined; stability in the region is the primary interest of Constantinople which sees these provinces as an important commercial battleground. Some of the more learned in both the capitals of these Sultanates and in Constantinople have been calling for the reconstruction of the old Roman aqueducts so as to strengthen the local economy of the region but so far, these voices are not yet widespread.
Egypt:
Egypt is one of the primary benefactors of the revived trade between the Mediterranean and the Indian Ocean as the 'in-between', as well as the province which holds the vitally important Suez Canal. Wealthy, urban, and populous, some in Constantinople grumble that while Constantinople may be the gem of the Empire, Egypt has worked to swing the interests of the Empire southwards with its growing wealth. The old administration of Mamluks was abolished during the 'Great Re-organization' 50 years previously as they had repeatedly hampered Venetian efforts to increase trade, and the region is now directly administered by the Ottoman bureaucracy. Alexandria is the 2nd biggest city in the Empire, with Cairo at 3rd.
Ethiopia:
Despite a mixed century, Ethiopia has notably advanced as a regional power, and hasn't been so centralized since the height of Axumite power. Centered in the Highlands, Ethiopia has struggled to absorb the Oromo migrations but as a result of a booming export of raw goods, notably timber, to the port of Mogadishu via the conquered port of Massawa to fuel the Ottoman Indian Ocean fleet. Ethiopian merchants have slowly started to spread into the Indian Ocean and are also the primary middlemen of goods between the Funj/Luo and the Ottomans.
East Africa:
East Africa is something of a mixed bag. The coast is almost entirely dominated by the Ottoman Empire and its semi-vassal, semi-city state empire that's home to a multicultural mishmash of Turks, Venetians, Arabs, Indians, Swahili, Bantu, Ethiopian, Somali, and the occasional Greek. Trade dominates the economic life of the region, as the exchange of resources from the interior for Asian goods and military weapons occurs. This trade has seen to the rise of several small yet highly centralized martial kingdoms in the entire and around the Great Lakes area for the past 50 or so years, but this seems to be coming to a close as the people of the interior have been conquered into five or six kingdoms which the Ottomans have long rejected the idea of conquering, instead favoring keeping a careful balance of power in the region. Each of these kingdoms easily has the capacity to overrun the Ottomans' East Indian possessions but all recognize that favorable trade with the Turk is the means to achieve superiority over other rival kingdoms rather than wastefully expend resources, regardless of various Portuguese, English, and French promises to aid in their conquests. Trade between the coast and the interior is dominated by native Swahili merchants and as a result, Swahili is lingua franca of the region.
Sahel:
---I don't know enough about this area to do something. If I were to hazard a guess, either one centralized kingdom like the Songhai that the Morrocans never invade, or many competing kingdoms. More prosperous than they would be otherwise as they can balance the Europeans on the coast and the Ottomans through the Sahara for trade.---
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There. That should be enough AH Playdoh to make a Great Power.