On the question of Persian origins of the śākyas - I would tend to agree with the suggestion that they were probably Persian (and I have my own independent reasons for it), but that would not necessarily make the Buddha himself Persian - the Persian-origin people in India may have claimed him to be one of their own after his time.
The reasons that I have for regarding the śākyas as being Persian are as follows:
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The endonym of the Achaemenids (i.e. the name they called themselves in the Old-Persian language of their time) was “Xšāça” i.e. it sounded very close to the name śākya. This name is not found as the name of any Indian dynasty in the late-vedic period when the Buddha lived, and we dont know where that dynasty was either before or after the time of the Buddha (the śakyas, assuming they were Indian, have no documented precedence before buddhism, nor is their continuing presence attested anytime after the Buddha’s passing) . The Jain literature are also apparently silent about such a dynasty.
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Dr. Thomas Oberlies in his book “Pali: A Grammar of the Language of the Theravada Tipiṭaka” (pages 6-9) points out specific word forms in Pali that betray Persian linguistic origins, specifically from a language like Avestan. This was to be expected, for the Achaemenids had invaded north-western India about one or two centuries before the Buddha’s lifetime and their linguistic influence must necessarily show up in some kind of Indo-Aryan. The fact is both Gandhari and Pali show similar Iranic influences. Those influences are however not present in Classical Sanskrit and Vedic, which allows Dr. Oberlies to isolate Pali from Classical Sanskrit. Vedic and Classical Sanskrit due to their conservative grammatical and phonetic traditions appear to have resisted this lexical and phonetic influence.
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If we reject the above and say that Pali is entirely Indian, then necessarily it calls into question what language family it belongs to - as the word forms pointed out by Dr. Oberlies cannot have arisen in an Indo-Aryan language family (i.e. originating in Vedic). Why didnt such “foreign to Indo-Aryan” phonetic forms survive after Pali in later forms of Indo-Aryan - and what makes them unique to Pali (and Gandhari)?
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The comments of the Sanskrit grammarian Patañjali (circa 2nd century BCE) are relevant here. He says “mlecchaḥ ha vai eṣaḥ yat apaśabdaḥ. mlecchāḥ mā bhūma iti adhyeyam vyākaraṇam” (Ungrammatical word forms are not Indo-Aryan, they are mlecchāḥ i.e. foreign to Indo-Aryan India; therefore one should know the grammar to identify ungrammatical usages to avoid speaking like the foreigners). The foreigners that he was referring to could have been only the yavanas (greeks) or the kambojas (persians), both of who had their presence in India in the few centuries before his time. It wouldnt have been the greeks, because greek words were grammatically and phonetically far from influencing Indo-Aryan speech. However Iranian speech was not far, in fact Avestan and Old-Persian were very close to Old-Indo-Aryan and would have had exactly the kind of influence on Indo-Aryan that Patañjali speaks about here, and what Dr. Thomas Oberlies has provided evidence of from Pali. Gandhari being written in the Kharosthi script derived from Imperial Aramaic script (the official script of the Achaemenid Empire), and being a land under Persian rule for 2 centuries, and also being one of the languages of early Buddhism also shows the same Persian influence as Pali does.
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One may raise the question - how could Pali, being an eastern Indian language associated with Magadha be identified as a language with Persian influence. For gandhari at least, it makes sense as it was a northwestern Indian language. The answer to that question is that Pali is not an eastern-Indian language, it is now common knowledge that Pali is also a western Indian language close to the language of the Girnar Ashokan edicts (located in the Western Indian state of Gujarat).
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A curious fact about the Major Rock Edict 5 of Ashoka at Girnar is that it is the only one of his edicts that names the city of Pāṭaliputra. Exact copies of the same edict are found in at least four or five different other places across Northern India but everywhere else, the word Pāṭaliputra has been replaced by the word “idha”. My understanding is that this was done because the people of those places would not have perhaps recognized the name Pāṭaliputra (as it was a new capital city built evidently by the Mauryans themselves, or shortly before them). The earlier capital of Magadha was Girivraja (also called Rājagṛha). So Aśoka evidently expected the people of Girnar to know Pāṭaliputra (as it was evidently somewhere in the vicinity of Girnar) but the other locations where he had put up the same edict were not expected to know the new city, and therefore had to be omitted from their local copies of the same stone edicts.
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The above point also indicates that Girnar was possibly the original location of Ashoka’s edicts, as that would have given the opportunity to remove the word Pāṭaliputra before the same edict was inscribed at other locations.
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This further raises the possibility that Girnar was in Magadha i.e. it was Ashoka’s home territory which is why his edicts came up first there.
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Another king named Rudradāman (who lived about 3 centuries after Aśoka, also has left his edict at Girnar right next to Ashoka’s edicts, saying that the area was under the control of Chandragupta Maurya who make some improvements to the lake located at that location.
So we have this early evidence pointing to the idea that Girnar is related not just to Ashoka but even to his grandfather, the founder of the Mauryan empire i.e. Chandragupta, and it contains the only mention of the name of Pāṭaliputra in all of Ashoka’s edicts, and the Girnar edicts were his earliest copy of the Major Rock Edicts. All this in my mind makes it most likely that Girnar was the location of the historical Girivraja, and that the historical Pāṭaliputra was somewhere in the vicinity of Girnar. -
In the MN140, the Buddha is in Rajagṛha where a young monk says to the Buddha (the monk doesnt know the person he is speaking to the Buddha himself) - “Atthavuso, uttaresu janapadesu savatthi nāma nagaram” (there is, sir, in one of the northern kingdoms, a city called Śrāvasti) - evidently this means someone at Rājagṛha is not expected to know cities in the northern kingdoms, and more importantly, there is evidently a sure north-south orientation between Śrāvastī and Rājagṛha. Śrāvastī was in a northern kingdom (Kosala), and Rājagṛha is in a southern kingdom (Magadha). So if Rājagṛha is Girnar (see the above point), Śrāvastī can be expected to be well north of it, i.e. somewhere in or around the Punjab.
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Now Punjab is where the other EBT language (Gandhari) was prevalent in. So if Pali is the language of the western Indian state of Gujarat or thereabouts (as Pali is close to the language of the Girnar edicts), why wouldnt the language of Kosala (Punjab) be Gandhari? It seems to make sense. That is how both Gandhari and Pali appear to have western influences connected to Persian. Since writing originated in India from Persia at the same time, it would also then make sense that the canon was written originally in Kharosthi and Pali - which are two of the most important EBT languages, and they are both linguistically related to one another. That is also how Pali would properly be identified as a Magadhan language, not if Magadha itself was somewhere else in Eastern India.