Who is liable for a new hot water heater that burst?

The The issued you have is whether you are going to make a claim for defective workmanship or a breach of warranty/defective product.  Defective workmanship is where the plumber deviated from the average standard of care involved in the stallation proceess.  A claim against the manuafacturer is a claim that the water heater was defective.  I suggest as a practical matter that you hire another prumber to come out and inspect the water heater and determine which was the cause of the flood.  depending on the answer, you will know whether you want to make a claim against the plumber or manfuacturer or both.  I suggest that you hire a lawyer to speak to the plumber you hire to inspect the project and have the lawyer issue the letter accordingly.

Unless you have evidence that the plumber was negligent when installing the water heater or doing other work on the water heater, the plumber would not be liable.  Your lawsuit should name the manufacturer and the seller (store) and/or distributor where you purchased the water heater as defendants.  This area of law is products liability.  Products liability includes both negligence and strict liability. 

In addition to causes of action for negligence and strict liability in your lawsuit against the manufacturer, seller, and distributor of the water heater, you should also include another cause of action for breach of warranty.  The warranty may have been express and/or implied.  If there is a written warranty on the product, that is an express warranty.  If there isn't any express warranty on the water heater, there is still an implied warranty of merchantability which would require the water heater to comply with commercial standards of acceptable quality.