Hi there AniaBigda!
My apologies for the delayed reply. In reading through your post, I wanted to first check if it already exists as a function within Canvas or if there is something similar within the grade book. I found this guide on leaving comments via the grade book and this guide on the icons that exist in the grade book. Both seem to come close to your idea, but they do not mention an actual icon appearing in the grade book that denotes if a comment has been made. I do know that annotated comments do not leave icons in the gradebook either.
That being said, I do see the value in adding an icon to show that students have already received some sort of comment on their respective submissions. Not only would it make the commenting process easier for graders, it will also save them time. Whether it is annotated comments on a submission or comments in the side panel, it makes sense to have some type of icon in the grade book that denotes the fact that comments were made. That way instructors can ensure they are being fair to all students by leaving comments on all submissions.
Since this function you are mentioning does not exist in Canvas, I recommend submitting it as a New Idea for other Commuity members to discuss. This is how all the great new functions and improvements start within Canvas.
Before you can submit in the Canvas Ideas area, you will need to "rank up" to the "Community Member" rank. I see you already have a couple of posts in the Community so ranking up should be a simple process for a pro like yourself. Here is a guide on how to "rank up".
Once you "rank up" you will want to follow this guide on how to create new ideas. Feel free to copy/paste/paraphrase, into your new idea, anything I mentioned above with regard to the already existing functions and guides. That way, other community members will see that the foundations for your idea already exist and it is really just a matter of adding another icon in the gradebook.
I'm excited to see your new idea and all of the conversations it will strike up within the ideas page. I believe this function will save time for graders and instructors alike.
Best,
Trey