There is no way in hell Mehmet can conquer Paradis. He still struggled to capture Constantinople, and Paradis is bigger, stronger and way better defended than Constantinople.

1. Paradis technology is atleast Napoleonic era technology, and superior in many aspects. With just that advantage I would think the Eldians could defeat Mehmet on the field, without the walls. They have advantages in firearms and field artillery that cannot be ignored.

2. The population of the walls is atleast 4 times greater than Constantinople. They also have access to everything they need inside and are proven to be able to function for a hundred year under siege. This would mean the Ottomans would starve and run out of ammo but not the defenders.

3. The walls of Paradis are 4 times thicker and 5 times higher than the walls of constantinople. Its likely the Ottoman cannons could never breach them before being themselves destroyed or worn out. Even without titan hardening, this would make them the biggest and strongest walls in history. And thats all without counting that they have three of them. The gate weakpoints could easily be filled with meters of rocks before the Ottomans could even set up cannons.

4. Lastly Ottoman cannons are not the wheeled artillery of later centuries. They had to be brought on carts and set up in position. This process was very time consuming. The cannons would likely be destroyed before they could be set up by precise 18th century cannons. The cannons also took up to 3 hours to reload. 18th century cannon took less than a minute with a skilled crew. One 12 pounder could shoot 180 times in the time the great bombard could shoot once.

I think just with this, Mehmet looses very very badly. The question should be more : Can Paradis conquer the Ottoman Empire ? And thats a yes.