You would find Buddhist ideas in Advaita and other ‘Hindu’ philosophies because these were modeled on Buddhism, and mostly concocted by Brahminical revivalist to sideline Buddhism. Over a period of few centuries, they were able to do it, displacing Buddhism-one of the most advanced religion of its times-from its birthplace to the periphery. While Brahminical revivalist philosophies were ‘Buddhisoid’ in its nature, their application and intend was quite the contrary of their theories. The destruction of Buddhism from India established a horrible form of cultural practices in the whole Indian subcontinent and took India back to dark ages. I have written elsewhere that this is the singular most important event that impeded the progress of India as a civilization. The ruse of ‘Buddisoid’ Brahminical philosophies was to use the practices of Buddhism and recast them in their ulterior manner. Thus, they created myths making Buddha as a ‘reincarnation’ of Vishnu, and appropriated Buddhist worship practices as their own- but with a castist twist.
Advaitha philosophy looks like Semitic ideas because of later reinterpretation of it, inspired by the Semitic religions who were drolling at the ‘pagans’ of Indian mainland as subjects for their ‘conversion’ mission. Making a ‘semiticised’ Brahminical religion was the only way to compact the Semitic religions in their conversion spree. Thus, Advaithic Hinduism looks like Christianity, just as Buddhism looks like Advaita. They are copycats. Unfortunately, there were no piracy rules in those times to call their bluff!