I think it'd probably be more productive to discuss regions of Africa rather than try to create a homogenized answer for the whole continent. Also, let's recall that the OP specified no New Imperialism, not no colonialism at all.
Areas already colonized:
Probably more socially and economically developed, partially because they get a larger slice of colonial budget, partly because it is my understanding that some of the coastal trade posts (Lagos for instance) became less self governing after they were attached to larger colonial units. Algeria in particular will be poorer without much of its oil, though perhaps stabler with fewer berbers butting heads with the dominant Arabs.
Independent North Africa (how are we counting Ottoman Libya?):
IOTL they were some of the last African polities to be colonized and some of the first ones to regain independence, and in the case of French Morocco, Tunisia, and Egypt the Europeans governed relatively lightly. So generally it'll be not too dissimilar to OTL, with economic development probably trending closer to southern Europe rather than their OTL counterparts.
Independent coastal (and near coastal) Africa:
Really varies. Being integrated into the global economy, comparisons with South America and Thailand may be apt. Do note however that no "New Imperialism" does not discount old imperialism continuing. Strategic sites like Djibouti are likely to be gobbled up all the same, Kongo's terminal decline and dependancy on Portugal for basic government functions probably means its fate is already sealed, and if a certain sultanate on the Swahili coast doesn't cool it with the slave trade Britain's likely going to still set a certain world record.
So generally, at least as developed as OTL, probably more.
The Sahel:
Also integrated with the global economy, but land locked. Paraguay, Bolivia, Nepal, Ethiopia, and Afghanistan are relevant OTL points of comparison. Some of the Sahelian polities had large urban centres (by pre-industrial standards) and tend to have large cadres of literate individuals owing to the importance of the Islamic clergy to most of these states. There may be a recipe for big success stories here. However by the late 1800s many of these polities were in steep decline, for instance:
Yeah, when being conquered by a brutal theocratic warlord and slaver constitutes an improvement... yikes. Additionally, Sahelian states seem kinda fragile. Both Rabih's empire and the Sokoto Caliphate would be conquered after losing a single battle, and, for an earlier example, Songhai collapsed after losing a single battle to Morocco in 1591. I'm not sure if these were just circumstance or if Sahelian states structurally lack the capacity to replace losses. If it's the latter then the region may well end up being very fluid, and easy prey for the coastal states (Morocco returns to Timbuktu?).
Probably better than OTL, I mean with most of colonized Africa there's at least a "but they built railroads" argument to be made for the colonizers, but French didn't even manage that here lol
Interior Subsahelian Africa:
Ah yes the part of Africa that actually was blank on most maps prior to the late 1800s. Some parts of these regions really are quite isolated and tribal in structure. Certainly there were some trade routes going through here, but they were generally controlled by the powerful coastal states, and often doubled as invasion routes for parties of slave takers. Now there are some more advanced polities here and there, particularly around the Great Lakes. Some of these polities, like Msiri's Yeke Kingdom actively sought diplomatic engagement with the Europeans, and may well end up being early modernizers.
So what do these polities and peoples joining the globalized world order look like? Much of this thread, and admittedly much of this post, has treated contact with the outside world as an unambiguous good. Yet I'll point out that the Meiji Restoration required a civil war. For many places, eventual improvement will only come after a period of pain and hard feelings. In this part of Africa in particular things are likely to be about as bad as OTL. I don't for one second think that Arab-Swahili colonization of the interior would be all that much less exploitative than that of the Europeans. Additionally, even without the scramble for Africa parts of this place may not be off the menu. Portugal had briefly ruled *Zimbabwe in the 1500s, and had always had linking Angola and Mozambique via land on their to-do list. Zimbabwe's highlands have ideal soil, are known to be free of malaria, and iOTL were conquered by a very small force. The possibility of it becoming a settler colony of Portugal, or Britain, or a Boer Republic can't be entirely discounted.
But I'm no expert on the subject.