The offline execution of Office Scripts is possible through Power Automate platform, which allows end-users to automate their Excel related tasks as part of a larger flow. An Office Script can be invoked against any Excel file on OneDrive/SharePoint site and data can be passed to a script and script can return data out of Excel that can then be integrated across other apps.
See here for more details: https://learn.microsoft.com/office/dev/scripts/develop/power-automate-integration
Other scenarios you site such as ability to invoke Office Script via browser console or from other parts of Excel app is not supported. There is one aspect that is of interest to us, which is to allow web add-ins to invoke Office Script. Please feel free to add feature asks here: https://excel.uservoice.com/
Examples of offline scenarios with Office Scripts:
1. https://powerusers.microsoft.com/t5/Power-Automate-Cookbook/Cross-Reference-and-formatting-two-Excel-files-using-Office/td-p/728535
2. https://powerusers.microsoft.com/t5/Power-Automate-Cookbook/Excel-and-Microsoft-Forms-integration-using-Office-Scripts/td-p/728183