Interesting question. From my knowledge and research it seems that this is more of a history of art question than something specifically related to scriptural reference or spiritual attainment. No reference is made to Jesus having a halo in the Bible but the earliest depictions of him in art have the halo. So tracing this back we find some of the earliest depictions of the halo in the classical world.
Homer describes a more-than-natural light around the heads of heroes in battle, Depictions of Perseus in the act of slaying Medusa, with lines radiating from his head, appear on a white-ground toiletry box in the Louvre and on a slightly later red-figured vase in the style of Polygnotos, ca. 450-30 BC, in the Metropolitan Museum of Art. - Wikipedia
... and this may go back further to ancient Egypt and the Sumerian cultures who worshiped Sun gods who had depictions of Sun disks around their heads. This in turn influenced early mystery schools in Greek and Roman culture such as Mithraism, where Mithras is often depicted with a halo.
In addition to classical sources, the sun disk found in Egyptian crowns may have been an early manifestation of a halo-like form. - History of the Halo in Art
So how does this relate to its depiction in Buddhism? You make reference to Buddha's Greek makeover and it seems some scholars assume this is the period when Hellenistic culture, spread through Alexander the Great's conquests, influenced, among other things, art in the East. This relates somewhat to this question.
There exists an aesthetic tradition of depicting the Buddha with a halo. One of the most compelling facts about the Buddhist tradition is its involvement in the Hellenistic world. Being born out of the Hindu religion in India, much like the Christian religion being born out of Judaism; the aesthetic tradition of the Buddhist religion is rich with symbolic language indicating that the Buddha is a spiritual heavenly being. This was not always the case. We can think of the Buddhist aesthetic tradition, similarly to its teachings, as being a very complex evolution of Hellenistic principles and cultural awareness. - Religion, Art and Myth-Making: The Halo as an
Aesthetic Expression of Ultimate Reality
Circumstantial evidence seems to point to Western influence in the halo depictions in Mahayana Buddhist art.
Around the first century CE, the regions of present-day Afghanistan, Pakistan,
and North India came under control of the Kushans…Exact dates are uncertain, but they ruled from the first to the third century CE. The beginning of the long
reign of their most illustrious king, Kanishka, is variously dated from 78 to 143 CE. Kanishka‘s patronage supported the building of many stupas and Buddhist
monasteries…Buddhism during this period underwent a profound evolution that
resulted in the form known as Mahayana, or Great Vehicle. This vital new
movement, which was to sweep most of northern India and eastern Asia,
probably inspired the first depictions of the Buddha himself in art (Stokstad 322, 323). - Art History a View of the World (Marilyn Stokstad)