This is an interesting question. I'm not sure that I would count Habesh as an Ottoman periphery. Apart from a couple of fortified posts on the Red Sea, and a few military expeditions, the Ottomans didn't really go into Sudan or Ethiopia (even though they marked it as a province on some of their maps). I would see their African periphery more as southern Egypt. Or even, from the perspective of many in Constantinople, Cairo itself was seen as a periphery.

Anyway, in terms of how the Ottoman elite viewed the people on their peripheries, one of the Ottoman authors who most wrote about this was Evliya Çelebi. You can find sections of his travelogue (Seyahatname) in English. There's certainly some elements of an "Orientalist" attitude - he exoticizes people he finds on the European frontiers (Albanians etc) and on the African/Asian frontiers. But it's quite light-hearted and in places downright surreal (he has a bizarre passage about Egyptians wrestling crocodiles to have sex with them). There's definitely the assumption of superiority of his own people (the Rumis, i.e. the Turkish-speaking Ottoman elite of the Balkans and western Anatolia), but I don't get the sense of a binary east/west division of the world that you find in Orientalism. It's more a kind of typical chauvinism - for him the world is a crazy patchwork of peoples, all of them fascinating, some of them advanced and some of them backward, but none of them quite as special as the Rumis.

In the late 19th century the Ottomans did develop an ideology much more like Orientalism - there was an interesting article about this in the AHR a while back, by Ussama Makdisi. Essentially, as they attempted to modernize and partly westernize the empire, they adopted aspects of the European model of colonialism. They were keen to be counted as a European colonial power (this was important within European politics, as it would exempt them from being objects of colonization). And they started to see the empire as an advanced, superior Turkish people ruling over backward Arabs, Kurds, Albanians, Bulgarians, etc. That then starts to look quite like Orientalism - it has the binary division between Us and Other, the hierarchy, the exoticizing.