Met Adi Shankara Veda Vyasa

Why does Adi Shankaracharya say that magical powers can only be obtained through the Vedas?

Yes, there are different types of Havanhoma and Yagya to achieve Siddhi, but there are different types that we generally do not do.

There have been times in history when an entire race of mystical Nagas were wiped out in a yagya directed by Raja JanamaJeya, the son of King Parikshit, who was himself the son of Abhimanyu and whom you should know was himself Son of the legendary Arjun was from Mahabharata. So here is the story of Wikipedia:

According to legend, Sarpa Satra, or serpent sacrifice, was a yagna performed by Emperor Janamejaya of the Kuru Empire, who rose to the throne of Hastinapura after the death of his father Parikshit. Legend has it that Parikshit, the only descendant of the Pandu family, son of Abhimanyu and grandson of Arjuna of Mahabharata fame, died of snakebite. He had been cursed by a sage to die like this, and the curse had been perfected by the serpent chief Takshaka. Janamejaya had a deep grudge against the snakes for this act and so decided to wipe them out entirely. He attempted this by performing a great Sarpa Satra - a sacrifice that would destroy all living snakes. At that time, a learned sage named Astika, a boy in old age, came and intervened to stop the yagna. Astika's mother Jaratkaru, also known as Manasa, was a Naga and father was also Jarakaru, a holy Brahmin. Janamejaya had to listen to the words of the learned Astika and free Takshaka. He also stopped the massacre of snakes (nagas) and ended all hostility with them. From then on the snakes (Nagas) and Kurus lived in peace. ]]

See? Similarly, at the beginning of Kaliyug, yagya was performed to kill many malechas that were almost extinct, but then more malechas were created by Lord Vishnu himself at the behest of Kali, who would worship him and propagate Kaliyug.

There are similarly many aspects that are unknown to me, many, many things that we cannot fathom. But that's how it should be, it's Kaliyug.

They disagree, yoga is part of the Atharva Veda, but they may lack the knowledge or insight as they have never had to sit on other branches of the Sanatan Dharma so there is confusion. What we read is not the whole story, there are always untold aspects.