iOS and Android both have Focus Mode:
https://blog.google/products/android/android-focus-mode/
https://support.apple.com/guide/iphone/set-up-a-focus-iphd62...
I guess I don't use this feature when having a conversation with another person because it would require me to get out my phone and change modes when the conversation begins. That's too much of a barrier. In some settings, though, like when going to watch a movie in public, there's a dedicated window where people are expected to shift their phones to a socially acceptable mode. I do respond accordingly in those situations.
With AR, it would seem this process could be automated through facial recognition / voice detection. If there was a setting that said, "Don't notify me of text messages when the system detects I am conversing with another person. Do this automatically" then it seems quite practical to have that enabled. It also seems reasonable that it would be implemented because the concept of "disable notifications temporarily" already exists on phones.
Of course, some people will feel like these changes reduce the humanity of the interaction because you're letting the device do too much of the work and others will disagree and say that the tech is just helping automate and improve a task they were already performing. Both camps will have fair points.
These sorts of behaviors which augment the conversation seem distinct from concepts like "be shown new text messages while mid-conversation" which I do think should be able to be silenced and conveyed as being silenced.
I did make good use of Google Lens when traveling to France last year. I found myself engaging with the world by looking through my phone's camera frequently as it made understanding restaurant menus much easier.
I can see a future where people use AR, there's a setting that indicates "full focus" vs "distracted", and people will ask others to stay in "full focus" mode when talking. This would minimize the number of notifications the user receives in an effort to lend focus to the conversation.
It'll be the same general expectation as what you're describing, but with a step towards concession and acceptance of the tech.
There will also probably be an in-between period where people who remain glued to their phone try to take the morale high ground against those who are using AR goggles by saying they're giving more focus to the conversation :)