There is a standard for browser extensions. I build also browser extensions before the standard. So you can build now a browser extension that works in Chrome, Firefox, Edge and Safari. But indeed, you can also use some specific api's for only a single browser. That is really bad, like you build a site only for a single browser. But the base should be compatible. And because you always can see the extension source code, you can modify a version for your own that works well in your browser. (And you can share it again off course)