The most critical components of a Faraday cage are continuous conductive material around whatever you're putting inside it and an insulation layer (a layer of cardboard will do, plastic or air works well too). There's a school of thought that suggests another layer of continuous conductive material on the outside, insulated from the inner layer. Any devices being protected should not touch any of the conductive material.
A large steel toolbox (often called a "job box") could work as the outer layer, although I'd be careful to make sure that the lid was tightly fitted and well-connected electrically to the main body.
My expectation is that something like a Carrington Event would damage or destroy large electrical grid transformers, along with anything else connected to long conductive wires. Smaller grid transformers connected to shorter wires may or may not be affected. Based on what I've read -- I'm certainly not an expert -- complex electronics within cars and small devices are more likely to survive than not.
Certainly, a close, strong EMP would damage or destroy almost any electronic device.
I very largely agree, except that I see no need for an inner insulating layer. All parts of a Faraday cage will be at the same voltage and it matters not if the contents touch the inner walls.
A steel "job box" would give a good degree of protection but I would still prefer a second inner container as a second line of defense in case the hinged lid of the outer box gives imperfect protection.
These job boxes are often used to protect expensive tools against theft. Much better than a trash can in this respect. Security is good, no point in protecting supplies against EMP if a thief takes them instead.
A utility transformer connected to long power lines would probably be destroyed by a Carrington event and would almost certainly be destroyed by an EMP.
A spare utility transformer in the power companies stores and not connected to anything should survive a Carrington event.
A spare utility transformer in storage MIGHT survive an EMP if prepared by connecting all input and output connections to each other and to the steel tank. The tank IS a reasonable Faraday cage and connecting each end of each winding to the tank SHOULD prevent damage. Utility transformers are designed to withstand much greater voltages than domestic electronics.