Do I just auto battle through this entire game
Yeah, with a few exceptions. You can hit Y to attack before your ATB bar is completely full if you want to finish off an enemy. You can also manually do a few actions here and there.
The bulk of the gameplay is broader strategy management of the paradigms, and items.
To understand the philosophy that led to the creation of this battle system, put it in the context of the rest of the FF series. For FF 1-10, 99% of the time you beat enemies by just hitting X to attack. Occasionally you'll find an enemy obviously weak to fire, and then use your fire spell. Occasionally you'll be low on HP and hit a cure spell. After the battle you'll use an ether to replenish your MP, or a tent. That's the whole game basically, for the whole series, with a few boss exceptions requiring more strategy.
FFXII takes it a step further and literally automates everything through gambits. You don't even have to hit attack anymore, you just automatically attack. If an enemy comes up that's weak to fire, your group automatically knows to do that. It knows to do anything you tell it to, and the game runs on auto-pilot as you designed.
XIII tries to inject a little more action and interactivity into the gambit system from FFXII. What most people don't get is that each paradigm is a pre-built gambit. When you're on commando, you're going to do physical attacks, prioritize anyone in break status, and use blitz or ruin when enemies are in groups. That's your 3 gambits basically that it does on its own. If you want to switch to different gambits, you have to manually switch to the other jobs and they'll have other pre-built in features. If you want to upgrade the efficiency of your gambits (paradigms), then use libra and you'll learn an enemy weakness. Once you know an enemy is weak to fire, it will add that knowledge automatically to upgrade the efficiency of your gambits and use fire on that enemy. The end result is similar to FFXII, but there's more player interaction as you have to constantly toggle between multiple paradigm combinations to keep the correct gambits going.
You're like the commander sitting back and managing the flow of the battle, but not each individual action requires your input. Some people hate it, but I thought it was awesome. Combined with the level cap, it's got some really challenging and fun fights where you have to manage debuffs, buffs, healing, tanking, breaking guard, then damage dealing. Basically everything you'd want in a FF, just faster and streamlined.