Strictly speaking Buddha was not a royal price but scion of an aristocratic family. As a comparison think of someone born in a patrician family of Rome when his father is a Consul of Rome. The Wikipedia article has good details about the Shakyas: https://en.wikipedia.org/wiki/Shakya
Is that so?
It was propheised at his birth (so the legend goes) that he would either become an enlightened teacher, or a "wheel-turning" world monarch (chakravartin). That doesn't prove he wasn't a royal prince, but then I guess I'm not sure exactly what a "prince" is.
In an oligarchy you can still have powerful military rulers "whose chariot wheels roll everywhere"
To continue the comparison with the Roman republic. Consuls where great leaders bestowed with great power and honoured for their military successes. The Roman republic had a taboo of monarchy, one that Caesar himself played with dangerously and which got him killed.
Prince comes from princeps (the first), a title used by the Emperor Augustus.
> Most modern scholars believe he was most likely born sometime around 480 BC or thereabouts in Śākya Gaṇarājya, an oligarchic state in the northern Indian subcontinent and he most likely died sometime around 400 BC or thereabouts.
Siddhartha Gautama was born in present day Nepal, in the city of Kapilvastu in the Lumbini region. There are archaeological remains of the palace where he was born along with scriptures explicitly matching the origins and design.
The article also goes to great lengths to emphasize a lot of details are nebulous, however they are documented well since the Buddha was a royal prince. For that reason not sure where the idea that the depiction of Chinese Buddha should be accurate is insinuated either.