What are they going to do with the Tower of Babel?

They could leave it as they did with Doma Castle, but the whole thing is still a liability and a symbol of the suffering of the Garlean people. Thousands of Garleans, unfortunate servants and conscripts, died or were tempered to build the huge ominous tower. I wouldn't put it past the Garleans bringing the tower down.

However, there is an additional factor now, in the Lunar Teleporter. The Tower is now a supposedly dependable means to get to the moon. It was reliable enough that the Sharlayans adjusted their plans to try to get people to the moon through the teleporter, although it failed due to the Final Days.

The Tower is basically how the Loporrits came down to help us, so in a way it helped save the world by giving us access to their expertise. I wonder if perhaps the Loporrits could use their technology to 'remodel' the tower in exchange for allowing the Lunar teleporter to remain? Or perhaps that's too much to allow the tower to remain a fixture in Garlemald. The towers of Garlemald have shown up in past maps, whether in Stormblood or in its current form in Endwalker. I wonder if they'll keep that spiky incarnation of the towers in future world maps. If they make any changes, it'll have to be something in the MSQ or mandatory content - otherwise they'll have to put in different maps.
Stormblood.

Endwalker.