Ho-oh and the burned tower are some of the franchises early attempts at world building, Gen 1's story was really simple (it was a Gameboy game after all), but since Gen 2 was on the GB colour, they had a bit more space to flesh things out, so they could actually give a bit more backstory to its legendary Pokemon.
They didn't really make it clear in this episode, but there's only one Ho-oh, and people from Johto worshipped it because it's a pheonix that can resurrect the dead, also in the games it wasn't a war that burned down the tower, 150 years ago a lightning bolt hit it causing most of the city to be razed to the ground for three days before a mysterious rain put it out. I'm not sure if you remember, but Ho-oh was the mysterious Pokemon Ash and Pikachu saw at the end of the very first episode when they finally made a connection, they've hinted at Ho-oh a number of times throughout the series because of that as a sort of mystery that inspired Ash. The Pokemon company has released a number of short series animating key moments from the games or important lore to celebrate big anniversaries, I might need to sponsor some in one of the reaction streams, they have really pretty animation.