There is only one file type that uses the .LOCALSTORAGE extension:
WebKit Local Storage Data File
A LOCALSTORAGE file is an application support file created by web browsers that use WebKit, which include Google Chrome and Apple Safari. It may contain browser settings or local data for a browser extension (plug-in) and enables extensions to store a local cache of user data. LOCALSTORAGE files are saved in an SQLite database format and can be opened by SQLite programs.
Local storage is useful for extensions such as Chrome browser games. For example, the game Angry Birds stores saved game information in a LOCALSTORAGE file.
Chrome for Windows stores extension information here:
[user]\AppData\Google\Chrome\User Data\Default\Local Storage\
Chrome for macOS uses the following location for extension information:
~/Library/Application Support/Google/Chrome/Default/Local Storage/
Updated: August 20, 2019