How can I make an extension that works in Chrome work in Firefox as well?

I have an extension and it works on Chrome just fine. However, when I add the “browser_specific_settings” in manifest.json and try to make it work on Firefox, it doesn’t do anything. The code is available here: My extension is supposed to redirect Google searches to a private alternative, like DuckDuckGo and Startpage.

Also, there is an extension which does similar things as mine and this one works just fine on both Chrome and Firefox. The code is on: This extension redirects non private services, like YouTube and Twitter, to a private alternative.

I’ve just tested current version from your github page (using "web-ext run" command) and it works fine, my search was correctly redirected to DuckDuckGo and there are no errors in the console:

13:18:00.397 Webconsole context has changed
13:18:11.100 search:  q=hello background.js:77:13
13:18:11.101 Redirecting "" => "" background.js:98:15
13:18:11.101 Details 
Object { requestId: "112", url: "", originUrl: undefined, documentUrl: undefined, method: "GET", type: "main_frame", timeStamp: 1604837891071, tabId: 3, frameId: 0, parentFrameId: -1, … }