Does the end user of my application need to install browser extensions?

If you have integrated with Whatfix using the JavaScript embed method, your end-users do not require any browser extension.
Your end-users need the browser extension only if you don't have the access to the application code and cannot use the Javascript embed method of integration. When your end users require a browser extension, it's usually an internal use case and the deployment of the extension is done en masse as part of an IT policy.