I would really like to know more sources on your basic premise of Mani regarding Axum, China, Rome, and Persia as the great empires of the time, OP. Not to discredit geriatric and German writing authors, but the only credited source I could find to the premise is from "Kephalaia. Mit einem Beitrag von Hugo Ibscher," a 1940 piece written by Jakob Polotsky, et al. My lack of German and Farsi prevents me from finding more info. However plenty of non-scholarly sources on the matter are available. Anyway...

The late preeminent British scholar on numismatics and northeastern Africa, specifically Ethiopia, Dr Stuart Munro-Hay wrote a compelling book on ancient Axum's rise to international power. Of the many keys possible for the nation's ascendency is something that is all too similar to today's day and age: strategic geography, good climate for crops, and a stable economy to create a universal currency. Long before and certainly after their conquest of the southern Arabian Peninsula in the 6th century, any traders going through the Red Sea from Rome (ie, Alexandria), Persia, the Indian subcontinent, and further abroad would cross through Axum's territory. This ideal location would act as a trade hub where a unique Axum coinage would be accepted by people of many varieties, replacing the need for bartering within Axum and without. It's this environment that:

"led the Persian religious leader Mani to label Aksum as the third of the kingdoms of the world in the later third century; and something of this reputation is substantiated by the production of an independent coinage (Ch. 9) at about this time. It paralleled the country with the few other contemporary states with the wealth and political status to issue gold coinage; Rome, Persia (to a lesser degree), and, into the third century, the Kushana kingdom in northern India" (Munro-Hay, 1991: 13).

A regulated and government controlled currency was a rare thing at the time, for it to be accepted and used internationally is indicative of how affluent Axum was from king Endubis' reign circa 270 CE to the early decades of 600 CE. This is also the first known coinage from the African continent. But besides location, why would their currency be trusted? By pandering to their anticipated audience!

During the time of king Endubis of Axum(contemporary to Mani), the earliest recorded coin were gold pieces at 2.70 grams, concurrent --although intentionally not the same weight-- to the Roman aurei. Somewhat surprisingly, as an addition to their referential weight, "At first, the language selected for the coinage legends was Greek rather than the native Ge'ez," to which Munro-Hay claims is an "obvious reminder that the purpose of the coins was to participate in the trade with the Graecised Orient"(Munro-Hay, 1991: 154). The archaeological evidence suggests that Axum tried to actively emulate the current rates of their Roman neighbors, for another example, Axum adjusted their "heavier `tremissis' of c. 1.60g when the Romans reduced the weight of their tremissis to the true third of a solidus, with a theoretical weight of about 1.51g under Theodosius I in c.383"(Munro_Hay, 1991: 158). Purposefully inflating their value to create a sense of "a theoretical purchasing power slightly in excess of its real value"(Munro_Hay, 1991: 158). Citing "seignorage," the author posits that the reason why Axum's coins were simultaneously intended to be exchangeable with the ultimately superior Roman coins (financially speaking) but also slightly heavier was to protect it from destruction once outside of the country. Much like in academia, they used outside, 'peer reviewed' references of the Greeks and Romans to build up their position of legitimacy.

Appropriately sized for trade, with denominations available in gold, silver, and bronze, endorsed and produced by a weighting system that evidently followed and linked itself to the "Romano-Byzantine monetary system," Axum's trade based economy and government sanctioned coins "could pass easily in both local and external transactions, so long as the standard conformed" (Munro-Hay, 1991: 151). For Mani, the internationally rising Axum would be a nation that directly influenced merchants throughout the Persian world with the rare example of minted coins accepted throughout northerly Indian Ocean trade routes.

Munro-Hay, Stuart. 1991. "Aksum: An African Civilisation of Late Antiquity"

edit: Clarification editing.

I am interested in hearing a response to this as well, and tried to find previous discussions on the topic. Unfortunately, I could only find a scattering of tangential answers. I hope this helps sate some curiosity while waiting for a historian to respond although I could only find connections between Rome and Axum.

u/khosikulu responded on this post speaking on just how far south into Africa Rome's influence had reached.

That said, there is one area where Rome was certainly known in ancient Africa south of the Sahara: the Nile Valley and the Horn, and perhaps as far south as present-day Tanzania or Kenya. The Periplus of the Erythrean Sea (Red Sea, really) does mention trade out via that sea to spots on the African coast, including the entrepots of Adulis (for Aksum) and Rhapta (on the later Swahili coast); Roman Egypt's Christianity was the root of Aksum's (via Adulis), and so on to Ethiopia's.

u/Commustar also has a comment talking about how the Western Roman collapse effected Axum and talks about ties between Axum and the Eastern Roman Empire (the Byzantines).

Later Christian histories locate the fifth century as the time when the Nine Saints traveled from Syria to Axum, introducing the Syrian and Egyptian monastic traditions to Axum. These histories are confirmed by the archaeological record that shows the construction of several monasteries (or re-purposing of older structures into monasteries) in the Ethiopian highlands in the fifth century. These Nine Saints are also credited with bringing the Greek version of the Bible with them to Axum.

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The historian Procopius mentions a war between christian Axum and the jewish Himyarite kingdom (in what is now Yemen). From Procopius' work, as well as analyzing Axumite inscriptions, a tentative date for this war can be given as occurring between 520 and 525 AD. During this period, coinciding with Justinian's wars, there are also several recorded diplomatic exchanges between Axum and their Byzantine allies.

Damn, I wish we got even more responses and interest. Such a grossly overlooked historical subject IMO.