If permissions are to be checked, you always have to test them with the compiled app (APK).
As @TIMAI2 said, WRITE_EXTERNAL_STORAGE is sufficient as it implicitly grants READ permission.
Btw, these are (all) the permissions declared in the Companion APK:
Permissions AI2 Companion
<uses-feature android:name="android.hardware.bluetooth" android:required="false"/>
<uses-feature android:name="android.hardware.location" android:required="false"/>
<uses-feature android:name="android.hardware.telephony" android:required="false"/>
<uses-feature android:name="android.hardware.location.network" android:required="false"/>
<uses-feature android:name="android.hardware.location.gps" android:required="false"/>
<uses-feature android:name="android.hardware.microphone" android:required="false"/>
<uses-feature android:name="android.hardware.touchscreen" android:required="false"/>
<uses-feature android:name="android.hardware.camera" android:required="false"/>
<uses-feature android:name="android.hardware.camera.autofocus" android:required="false"/>
<uses-feature android:name="android.hardware.wifi"/>
<uses-permission android:name="android.permission.READ_CONTACTS"/>
<uses-permission android:name="com.google.android.googleapps.permission.GOOGLE_AUTH"/>
<uses-permission android:name="android.permission.GET_ACCOUNTS"/>
<uses-permission android:name="android.permission.BLUETOOTH_ADMIN"/>
<uses-permission android:name="android.permission.NFC"/>
<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE"/>
<uses-permission android:name="android.permission.ACCESS_FINE_LOCATION"/>
<uses-permission android:name="android.permission.ACCESS_COARSE_LOCATION"/>
<uses-permission android:name="android.permission.ACCESS_NETWORK_STATE"/>
<uses-permission android:name="android.permission.ACCESS_WIFI_STATE"/>
<uses-permission android:name="android.permission.MANAGE_ACCOUNTS"/>
<uses-permission android:name="android.permission.VIBRATE"/>
<uses-permission android:name="android.permission.RECORD_AUDIO"/>
<uses-permission android:name="android.permission.INTERNET"/>
<uses-permission android:name="android.permission.USE_CREDENTIALS"/>
<uses-permission android:name="android.permission.ACCOUNT_MANAGER"/>
<uses-permission android:name="com.google.android.apps.googlevoice.permission.RECEIVE_SMS"/>
<uses-permission android:name="com.google.android.apps.googlevoice.permission.SEND_SMS"/>
<uses-permission android:name="android.permission.CAMERA"/>
<uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE"/>
<uses-permission android:name="android.permission.BLUETOOTH"/>
<uses-permission android:name="android.permission.READ_PHONE_STATE"/>
<uses-permission android:name="android.permission.ACCESS_MOCK_LOCATION"/>
<uses-permission android:name="android.permission.ACCESS_LOCATION_EXTRA_COMMANDS"/>
<uses-permission android:name="android.permission.READ_LOGS"/>
It doesn't make sense to test permissions with Companion, because they are always granted.
You have to know if they are declared in your APK (Manifest).