I think the article is misunderstanding what is happening (though to be clear I think the email is at fault for that). Google is making it so that app developers can integrate Gemini better by allowing Gemini to interact with those apps. There is a menu inside Gemini where you can switch these interactions on and off (Inside Gemini, click your profile in the upper right corner and press apps in the menu).

I'm assuming from the email that this will be enabled by default which is a choice they've made and which absolutely could be argued as invasive. That being said you'd actively have to use Gemini and have it be active on your phone in order for it to interact with those apps.

Assuming Google records whatever you do on your phone whenever you do those things, which many privacy minded people of course legitimately worry about and feel uncomfortable with to various degrees, this is not really anything but another way for your assistant to do more things. If they want to read your stuff that's not really dependent on a switch in the Gemini app.

So if you have Gemini entirely disabled I don't think this is relevant. Only if you actively seek to use it and do not want it to be able to integrate with external applications will these settings be relevant to you.