Do I need to replace my idler pulley, belt tensioner assembly, or both?

It would not hurt to change it,it has the same wear as the idler,

From what I read I believe it may not be your belt tensioner, The big question I have is HOW could your idler pulley fly off??? You might be dealing with a broken bolt. IF the idler pulley flew off then I would be looking for a cracked bolt that should be holding it on; which if it is broken could cause rattling and improper tension which could seriously affect the whole serpentine belt system. Primarily your alt, which won't allow you to drive your vehicle. Check the spin of all of the pulleys, It could also be bearings of your water pump that go out and kill the pulley's balance and hence tension, followed by all the belt. But once again I believe you should be looking for a cracked bolt.

I would change the belt, idler(s) and the tensioner. Get them all replaced and you won't have to worry about anything to do with the serpentine belt system.

The plastic pulley separated from the bearing of the idler pulley and that seems to be why it flew off. I am going to try replacing that first since it is only one bolt. That way I can see if the tensioner is also part of the problem and not have to risk a good belt since I will be replacing this one anyway. I would replace the tensioner assembly too, but it seems to be a bigger job on this Buick, so I would rather not if it doesn't need it.

Sometimes you have the option of getting a metal idler in place of the plastic one. I do not like plastic idlers.

All of my options for idler pulleys were the plastic type unfortunately. I just replaced the idler pulley and took it for a test drive. It seemed to run well and it is back to being quiet like it was a few months ago. I plan on replacing my serpentine belt as well, but it doesn't appear that there is anything wrong with the tensioner.