How to diagnose an A/C failure? What tools & procedures are recommended?

My first assumption would be that hitting the road hazard caused a leak.

Tools: most of the tools you need can be obtained as loan a tools from AutoZone. Some folks here would be concerned that you might contaminate the special hybrid oil using loaner tools though. IMO, you can clear them out with brake cleaner and be ok.

If your system already has dye in it, you can get a UV light kit from AZ to help find the leak.

I would put a set of manifold gauges on the car and look at the pressures and listen for the compressor turning on. If the pressure is very low, you surely have a leak, probably in the condenser. If the gauges show a decent amount of pressure, but the system isn't turning on, then you need to figure that out. Likewise, if the compressor is turning on but the car doesn't get cool, that's another path of troubleshooting.

If you can replace the damaged components, you'll need a vacuum pump to pull a vacuum before you recharge. You'll also need a tap to connect the cans to the manifold gauges for recharging. The proper fix also will involve replacing the desiccant, although I've had good success not doing that.

 

I was in the same boat with our '10, around this time in 2018, and the only tool I needed was my credit card. An evacuation/recharge at nearby dealership cost me $166.88 CDN.

{Of course when I booked on the phone IIRC they quoted $150, but when done they were trying for MUCH higher. We settled on the $166.88 after some rangling.)

No problems since.