Sensied, a Swiss company, is selling a shotgun designed specifically for EOD personnel called the S&F K1 Doorbreacher. It is a 12 gauge pump shotgun with an 11″ barrel and folding stock. The magazine holds five 2 3/4″ shells.
The company also sells versions of this gun for competition and other purposes.
Below is a video showing its use as a door breaching tool.
According to a friend who is an EOD tech in the US military, space is generally at a premium in the vehicles. He said having something compact can be a real benefit. Likewise, I could see where this would be just as useful for undercover law enforcement or anyone needing a shotgun that can store in a very compact space.
The company also sells a six round shell carrier. The carrier attaches to the top Picatinny rail, and hangs on the left side of the gun. It does not interfere with the folding stock.
Thanks to Lionel for the tip.