I’m implementing an application and they are providing their app through their Website, not from Google Play Console.

I just wanted to integrate Google Assistant into that application. All I need to do is run my application using the google assistant. I read in the documentation that this does not require adding any changes to the code, provided that the main activity is in the manifest contains:

 <activity android:name=".MainActivity">
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />
                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>

However, my application does not launch with Google Assistant. This gave me the assumption that the problem was that my application was not published in the Google Store. Could this be related to this?
Also, can I use Google Assistant in this case? Do I need to register the application in the App Actions console?