A Google Doc that was shared with me. I see:
How can I request "commenter access" to be able to make "suggest edit" in a Google Doc that was shared with me? In other word, I want the person to click on commenter as follows:
I don't want full edit access.
Unfortunately, the only way to request only commenting access in the situation depicted by the screenshots in your question would be to email them asking them to give you only commenting access.
If you don't have viewing access, however, there is a text field that allows you to send a message to the doc owner directly during the permission-requesting phase. There, you could ask for commenting access only.
