Regarding Jews, I reaffirm that the majority of their history is a complete fabrication, there is so very little archeological or cross-cultural evidence to validate any of their nonsense. There was indeed a nucleus of proto-Jews to be found in the Levant, the likes of which were encountered and conquered by the Babylonians, Greeks, Romans, and so on, and we have already associated this group with the expelled 'Akhenaton' and his Hyksos contingent, whose descendants surely influenced Persians and Phoenicians.
However, this patchwork coalition of Egyptian exiles dwelling in the Levant, were not even a remotely cohesive force, in political, religious, or ethnic terms. They constantly fought each other, borrowed and stole their traditions from the neighboring groups, etc, it was and is a complete mess. We can see hints of this strong division when Moses descends from the mountain, only to find his followers worshipping idols. This story is a simple allegory for the true reality of doctrinal differences manifesting, culminating in the equally allegorical separation of the 'tribes of Israel'.
The majority of the ethnic, historical and religious traditions and claims of Judaic writings, originates solely in the demented minds and scribblings of Pontic-Steppe dwelling 'Rabbis', who some way or another inherited the spiritual tendencies of what we now call 'Judaism'. The idea that Judaism (both its religious and ethnic content), is the result of a direct continuation of tradition and people from Middle Eastern 'Semites', is a complete lie. Much of the Judaic mythos, in its consciously understood, doctrinal and written form, is barely 1000 years old. But sure, the Abrahamic archetype is indeed primordial, and we can maybe see traces of it in the likes of Gobekli Tepe and Baalbek, and perhaps the later appearing proto-Zoroastrian Vedic Indian expatriates who you have mentioned. All -different and separate groups who latched onto a similar, primordial archetype.
In regards to the direct connection between the Hyksos expulsion from Egypt and European royalty, it's not something I have explored in depth, due to the veracity, or lack thereof, and general mania, of many of the sources involved in this narrative.
As for the association of European royal houses with the Hebrew traditions in general, many have peddled this narrative, and not just European royals, but entire peoples, from the Pashtuns of Afghanistan, to the Black Israelites of America. I view it as a simple method of empowerment and validation with little historicity involved. Whether it be the Merovingian-Frankish royalty claiming 'divine descent from David', or the poverty stricken African American claiming the same thing. When the Germanic tribes entered Roman land and converted to Christianity, they were eager to correlate this new faith with their own rulers for prestige, likewise, when the Pashtuns converted to Islam, they tried the same thing, so did the African American slave descendants, and so on, and so on. I view much of it as purely symbolic accusations, born from these people's forceful reconciliation of themselves and their own identity, with a new, alien faith.
All that said, there is certainly some truth to it all, once we cut out the insane narratives peddled by certain forces out there. You might be aware of the potential correlation between the mythical Egyptian Queen Scota, the Milesian-Gaels of Spain, and their settling of the eponymously named 'Scotaland' or Scotland. However, these myths all have a medieval origin, and it's impossible to see any clear cut correlation with earlier traditions, let alone any other supporting tangible evidence. Therefore, it could simply fit into the previously described paradigm, where these legends of 'Scriptural descent', spring up in peoples trying to correlate themselves and their own ethnogenesis, with the foreign religion of Christianity, the myths of which all play out in far away Egypt and the Levant. It is a powerful thing indeed when a populace believes their kings to be descended from the figures of their Holy Books, very politically potent.