The answer in this case is that no, permissions are not required in this case, as Diprendra indicated in his answer, since the application sends its requests as intentions through external applications and is not a direct request to the network from its application.
A bit of background:
The easiest way to find out if you need permission is to use your application on a test device. Does it work the way you intended? Do you get any errors without INTERNET permission?
If so, it is clear that you need it! If not (and in the case of this question), you do not need INTERNET permission.
Permissions exist as a security feature.
This permission:
public static final string INTERNET
Allows applications to open network sockets.
Constant value: "android.permission.INTERNET"
If your application needs network sockets, your application needs permission to use them. Just like that.
Add the bottom line to the manifest if you need permission:
<uses-permission android:name="android.permission.INTERNET"></uses-permission>
Permissions exist to protect the user, so it's about being at the forefront and not going into any intentions of your applications.
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