Tensioner on serpentine belt?

Normally no damage. Look at the assembly to see if the rear plate has separated from the arm and pulley. It typically takes a real lot of effort to take one apart, but there's a warning stamped on it to not attempt that. You'll never get it back together due to the really strong spring inside.

All you need to do is bolt it back onto the engine with the locating key set in the notch on the engine. You found the square to use a breaker bar or ratchet to rotate the arm. I prefer to put the belt on the tensioner pulley first, then pull on the atm, then slide the belt onto one of the higher pulleys. Often the generator pulley is up high, but even that can cause a problem because of the ribs and lip on the pulley. Instead of trying to get enough slack to get the belt over that lip, look for a different pulley, (usually an idler pulley), and make that the last one to slip the belt over. Those are smooth with no lip, so you need very little slack to get the belt on.

As a hint, the smooth back side of the belt always goes around smooth pullies, and the ribbed side always rides on ribbed pullies.

You will need to remove the belt from at least one pulley, otherwise you won't be able to seat the peg on the tensioner. Here's a photo of it. I'm pretty sure you didn't do anything with the bolt with the red arrow. That's on the back side where you can't get to it. It sounds like all that happened is the peg, (orange arrow), came out of the locating notch. That would have happened with quite a bit of force if the belt was still on it.

For the tensioner to be damaged, the black plate behind my blue arrow would have to have come off. They're built in such a way that you have to really mean it and put a lot of effort into getting it apart. That's a dangerous job because the spring has so much tension on it.

As a hint, when you reinstall the belt, run it around all the other pullies except one that has no ribs or a lip on it, including this tensioner pulley. Often there's not enough slack in the belt to allow it to be lifted over that lip on the front of the last pulley. There's usually at least one idler pulley that is smooth. It will be easier to slide the belt on one of those when the tension is released on the belt.