This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. U+1F960 offers a line break opportunity at its position, except in some numeric contexts.
The CLDR project calls this character “fortune cookie” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: cookie, fortune, prophecy.
This character is designated as an emoji. It will be rendered as colorful emoji on conforming platforms. To reduce it to a monochrome character, you can combine it with Variation Selector-15: 🥠︎ See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
A fortune cookie is a crisp and sugary cookie wafer made from flour, sugar, vanilla, and sesame seed oil with a piece of paper inside, a "fortune", an aphorism, or a vague prophecy. The message inside may also include a Chinese phrase with translation and/or a list of lucky numbers used by some as lottery numbers. Fortune cookies are often served as a dessert in Chinese restaurants in the United States, Canada, Australia, and other countries, but they are not Chinese in origin. The exact origin of fortune cookies is unclear, though various immigrant groups in California claim to have popularized them in the early 20th century. They most likely originated from cookies made by Japanese immigrants to the United States in the late 19th or early 20th century. The Japanese version did not have the Chinese lucky numbers and were eaten with tea.