Weren't there much less White people in East Africa than there were in the southern parts of Africa, though?
There were still enough of them to alarm the Ugandans, many of whom were aware of the Central African Federation of Rhodesia and Nyasaland (later Zimbabwe, Zambia, and Malawi) and its domination by white settler interests. Ugandans deeply feared the prospect, and recognized that the kingdom of Buganda's special status would have to be sacrificed in the interests of a new and larger nation-state. The King of Buganda demanded that Buganda be separated from the rest of the protectorate and transferred to Foreign Office jurisdiction, and the ensuing negotiations in 1900, although appearing to satisfy the British, were a resounding victory for the Baganda, ensuring that the Uganda Protectorate would remain separate from British East Africa and that the Baganda would be granted authority as tax collectors and administrators over their recently conquered neighbours, an offer which was attractive to the economy-minded colonial administration, for whom quelling the King of Buganda, who had declared war against the British in protest at the prospect of his kingdom being amalgamated with British East Africa in July 1897.
Quelling the uprising and fighting the war to subjugate Buganda in July 1897 (with the deposed king Mwanga II having fled across the border to German East Africa and declared his allegiance to the Germans, through which it was believed that the Germans would assert their own colonial claim over Buganda), though routine, had been extremely costly; units of the British Indian Army had been transported to Uganda at considerable expense. And a subsequent mutiny by Nubian mercenary troops, who had also been brought in by the British to fight against Buganda, was even more costly. This mutiny was only barely suppressed, after two years of fighting; and had the Baganda not allied with the British, and demonstrated their support for the colonial power, the British would in all likelihood have been ousted from Uganda by the Nubian mercenaries. As a reward for this support, and in recognition of Buganda's formidable military presence, the British negotiated a separate treaty with Buganda, granting it a large measure of autonomy and self-government within the larger protectorate under indirect rule. One-half of Bunyoro's conquered territory (the best half, with the Baganda conning the British into taking all of the worthless swamp and scrubland) was awarded to Buganda as well, including the historic heartland of the kingdom.
This empowered the Baganda chiefs to act as local tax collectors and labour organizers across the entirety of Uganda, to become culturally chauvinist subimperialist rulers and to carry out 'Gandanisation', rather than the British themselves imposing imperialism directly and carrying out Anglicization. It might have been possible for this to be avoided, but only by doing away with Buganda at this early stage, thereby ensuring that Gandan identity never arises. And in doing so, you'd either most likely lose Uganda, at least for a brief period, either to the Nubian mercenary leader, to the Germans, or to inter-kingdom conflicts. And even when the British did reassert control, bringing the Ugandan territories under its colonial dominion, they'd probably never recover to be profitable. In this scenario, they would probably merge Uganda with Kenya for the same reason that they merged Northern Nigeria with Southern Nigeria; the only possible way to pay for projects in Uganda, as with Northern Nigeria, would be by drawing upon customs revenues from Kenya. Unlike with Southern Nigeria though, Kenya wasn't nearly as profitable a colony, and the East African Dominion as a whole would most likely fail to break even as a result, running at a (more) substantial deficit.
The British would either want to get rid ASAP in the post-colonial era, quite possibly enabling Haile Selassie to add the East African Dominion to his sphere, and perhaps even expand the Ethiopian Empire southwards during or after WW2- or alternatively, the British would turn to Ethiopia themselves as a means to make the East African Dominion profitable for them, waging wars to add Ethiopia to it as a British conquest instead of an Italian one. Which would probably backfire for them quite badly, and result in the post-colonial re-emergence of an Ethiopian Empire covering the entirety of the expanded East African Dominion. Or alternatively, regardless of whether or not Ethiopia's a part of it, the Communist University of the Toilers of the East's most prominent African alumnus, Jomo Kenyatta (1932 class), would most likely become its most prominent alumnus full-stop ITTL ahead of Ho Chi Minh, leading a Soviet-backed Pan-African independence movement in a similar manner, which liberates and keeps the region united under a far larger and more powerful East African Soviet Union of sorts. And one can only imagine how different the Cold War might have been in such a TL, one in which African nationalism and the Black Rights Movement would be even more intrinsically linked with Communism and the Red Scare.
Most likely, the Portuguese Colonial War ITTL would be a far larger, far more devastating proxy war between the Portuguese colonials, who'd get the full military backing of its NATO allies ITTL (and a nuclear-armed South Africa, of course), against the Portuguese African independence movements, who'd have even more support and backing from the East African Union and the Eastern Bloc; and there'd be a very good chance of that conflict either becoming a bona-fide WW3 or the closest thing to it. This inevitable conflict would make the Vietnam War pale in comparison, with a similar or even greater anticipated proportionate death toll. As much as 7% of the pre-war population of Indo-China died in the Vietnamese War, twice the proportionate death toll suffered by the Chinese and Japanese in WW2. You'd expect the resulting African proxy War ITTL to take a similar or higher toll of 7-9% of the pre-war population of the affected swathes of sub-Saharan Africa (Eastern, Middle and Southern Africa); and if it did, you'd be looking at a death toll of between 9.5M and 12M people.
The anti-colonialist Communist common fronts in Africa would almost certainly win if it remained a conventional conflict, as they did in Vietnam, and in doing so, you'd probably have a Communist African Union covering the majority of Sub-Saharan Africa, extending to the Atlantic. But unlike South Vietnam, South Africa had nuclear weapons, and if the Apartheid regime was faced with the very real prospect being enveloped by TTL's Communist African Union, the chief supporter and instigator of the popular black insurgency against them, the South Africans would use those nukes, even if the Americans and NATO hadn't already done so by that stage to beat back the Red Tide. And even if it was only a limited, localized nuclear exchange, between South Africa and the East African Union of TTL, it'd still easily exceed the death toll of WW1. And with the increased anti-NATO sentiment which this conflict would most likely engender in the neutral bloc in the Cold War, the increased civil unrest among the black community of the USA and European powers involved? It might even put the eventual victor of TTL's Cold War in doubt...