2004 Prius, 296k Tl;dr, my drive belt snapped and the car was towed home (car did not overheat, but leaked coolant from water pump). Bought a new water pump and belt, only to snap the 12mm bolt for the belt tensioner during the job. The 14mm bolt on the actual pulley was loosened before attempting to take out the 12mm. Where I’m at: I used a bolt extractor to drill into the old bolt and remove it, but only got out a small piece, there is still another piece stuck in there. I’m considering taking off that entire metal bracket/mount that the pulley is attached to. I honestly have no idea how I would go about that and if I’d have to support the engine, since it looks like it’s connected to a motor mount. Any suggestions?
You are right, the "transverse engine mounting bracket" includes the idler pulley slot. That bracket is secured with four bolts, 41 ft.-lb tightening torque. You would need to put a hydraulic jack under the engine on the oil pan, to hold the engine up while that bracket is removed. If you really cannot remove the snapped bolt while the bracket is in place, then it will be necessary to remove and replace that bracket. Good luck with that process.
As a little PSA about nomenclature, when we talk about bolt and nut sizes, we use the diameter of the skinny threaded part. If you're looking at a bolt with a head that fits a 12 mm socket, under JIS standards, that's an 8 mm bolt (a/k/a an M8). If the socket that fits is 14 mm, it's a 10 mm bolt (an M10). The difference might seem pedantic, but mixing the sizes up not only makes replacements harder to find on hardware store shelves, it sometimes gets people into real trouble if they look in a torque chart by the bolt size to decide how much to tighten something.