Today it defaults to "Container" and cannot be adjusted via MM or part config. While it's not normally needed, for the parts with variable capacity it may help resolving the missing inventory issue.

Use the following MM patch to have the inventory added.

@PART[YourPartName]
{
	// One module per a dynamic seat.
	MODULE
	{
		name = ModuleKISInventory
		invType = Pod
	}
	// Add more modules as needed.
}

Every seat needs one inventory. Do not include the seats that are already counted in the CrewCapacity number. E.g. if the part in prefab has CrewCapacity = 1, and the part can deploy to contain up to 4 kerbals, then you should only add 3 pod modules. If you add more, it won't break anything, but the players will get confused, since they will see too many "Inventory" menu items in the editor.