The Mughal Empire is in the game, but you can't form it or release it yourself. The only way to get them is if the EIC fails to prevent the sepoy mutiny. The country is also named "Hindustan" rather than "Mughal Empire", but it is ruled by Bahadur Shah Zafar II, the last Mughal Emperor. I think if a Muslim country were to conquer India it would not form a state called the "Mughal empire", but rather just "India". It doesn't make sense to add the Mughals as a formable, but then again, there are some other dumb fantasy formables like Byzantium so maybe it can be one of those.
I had no idea Burgundy was possible. Paradox really needs to give Viccy 3 some achievement-hunting love and steer us towards some wacky playthroughs like this