How to lower or destroy a captured city? (Humankind)

Put a detachment on it and plunder. It even works with its own cities.
will not lower, but destroy for sure.

Mind_Flow
later it will be possible that city, as an outpost, to be attached to another city

Either loot, or get technology to connect other cities to the selected city, then it is automatically lowered to an outpost.

But it costs so much influence, attaching these, that it is easier to demolish

Yes, select a squad and press the plunder button from it. There is also an option to merge with another city, but this is closer to the middle of the game. And you can also give it to an independent people (or it only works with outposts, I don't remember)