A family of Microsoft word processing software products for creating web, email, and print documents.
If the template is on your local drive and you double-click it in File Explorer, it will open desktop Word with a new document based on the template -- that's the default behavior on the desktop. You can't get Word Online to do that, because Microsoft hasn't programmed the web version to do that.
The only other thing you can do is tell Microsoft what behavior you want in the web version. The article
explains how to do that, with a link to the feedback site.