In terms of the database, the Release Type is in relation to the console category. It has nothing to do with whether or not the people who made the item or software had a license agreement with anyone to make the product. So for a game that was released on physical media for a Nintendo console after the fact, if it is not an officially licensed Nintendo Product, it is an Unofficial Release.
No physical game should be set to homebrew. An entry in a physical category is for the item itself, not for the game content. See this text from the Advanced Guide:
Homebrew vs Unofficial Release
A homebrew that is released commercially for a console is considered to be an aftermarket or unofficial release in terms of the database. For a physical item, which is tracked in a physical game category, the context is for the item itself, not the data content.
Example: Pier Solar and the Great Architects (the game data) is a homebrew, but the products that contain the data is an Unofficial Release.