Schelling's familiarity with Upanishads was likely late, first German translation appeared in 1832, although there were earlier Latin and English translations, all of questionable quality. But he was enthralled by them and encouraged his student, Max Müller, to do a scholarly systematic translation, see Vedanta Society's Journey of the Upanishads to the West. It only came out in 1879, however, 25 years after Schelling's death. Here is from Müller's preface:
"My real love for Sanskrit literature was first kindled by the Upanishads. It was in the year 1844, when attending Schelling's lectures at Berlin, that my attention was drawn to those ancient theosophic treatises, and I still possess my collations of the Sanskrit MSS, which had then just arrived at Berlin, the Chambers collection, and my copies of commentaries, and commentaries on commentaries, which I made at that time. Some of my translations which I left with Schelling, I have never been able to recover, though to judge from others which I still possess, the loss of them is of small consequence."
Tesla also accepted the non-dualism of Upanishads enthusiastically when he was in his forties, but he got it from a different source. Skala's From Boskovic's fundamental theory in natural philosophy to generic technical innovations of Tesla describes it as follows:
"A big change in Tesla's world view took place after he met Svami Vivekananda, a high ranking Indian spiritual teacher, during the Congress of all world religions in Chicago 1893. Tesla became a true follower of the Vedic
philosophy including Hinduism, Taoism and Buddism and their picture of the nature ofUniverse.Tesla built the Vedic philosophy in his everyday life habits by practising yoga and becoming a vegetarian... After meeting the Swami Tesla
continued to study the Eastern view of the mechanisms driving the material world, Tesla also began to use the Sanskrit words Akasha, Prana, and the concept of luminiferous ether to describe the source, existence, and construction
of the physical universe.
Swami Vivekananda was a Hindu monk, a disciple of the Indian mystic Ramakrishna, and a major promoter of Vedanta and Yoga philosophies in the 19th century Europe. Interestingly, Max Müller also met with Swami in London in May 1896, which apparently inspired him to write Ramakrishna, His Life and Sayings published in 1898.
As for Upanisdhads' influence on Tesla's work, it is probably fair to say that it provided some general inspiration, but it is hard to trace it specifically to any of his inventions, Skala does not attempt it. And the OP quote reflects the then current hopes, widely shared, for "grand unification" of physics by an all-encompassing ether theory in addition to the Upanishads. Compare to Michelson's 1902 speech:
"The day seems not far distant when the converging lines from many apparently remote regions of thought will meet on this common ground. Then the nature of the atoms, and the forces called into play in their chemical union... the explanation of cohesion, elasticity, and gravitation — all these will be marshaled into a single compact and consistent body of scientific knowledge... one of the grandest generalizations of modern science ... that all the phenomena of the physical universe are only different manifestations of the various modes of motion of one all-pervading substance — the ether." [quoted from Kragh, Quantum Generations, p.4]
Ironically, it was Michelson's own experiment that played a large part in spelling the end of this grand vision.