It is possible to detect if a userscript is installed from the Chrome Store, but there is no way to do this purely from the Chrome Store. Here are some tips for doing this:
Check for Updates: Chrome Store provides an update notification feature for userscripts which uses an API call to check the current version of the installed extension or userscript. You can use this to tell if the userscript is up-to-date.
Look at the Manifest File: If the extension or userscript is registered in the Chrome Store, it contains a unique Manifest file with all its associated information. You can use this to check if the userscript is indeed present.
Inspect the extension code: If the userscript is available via the Chrome Store, you can directly inspect its code in Chrome’s DevTools. This allows you to check if the code is indeed related to the userscript, or whether the userscript has been modified by the users.
For more information, please refer to the official Chrome developers page: https://developer.chrome.com/extensions/userscripts.