Not quite what you're asking for, but you can see student replies to grading feedback all in one place in your Canvas inbox (not your email inbox, the inbox area in the global Canvas navigation bar). You have to toggle it from "inbox" to "submission comments" to see them.
Guide on submission comments in the inbox: https://community.canvaslms.com/t5/Canvas-Basics-Guide/How-do-I-reply-to-submission-comments-in-the-....
Unfortunately, messages in the submission comments area do not trigger the unread message indicator on the inbox icon.
The email notifications are the only way Canvas has to alert you of unread comments on grading feedback. This is a major frustration for our faculty too.