When you open the sidebar in Google Docs, you have the option of filtering the suggestions you see. As of now, you can select Grammar Suggestions or Sentence Suggestions from the filter in the sidebar.
To choose a filter option, click on the little filter icon in the sidebar and it will open the filter menu. Select the error category that you want to view suggestions from. Once you do so, the sidebar will show suggestions only for the selected category. Additionally, the underlines on the page will be shown only for the errors in the selected category. To see all suggestions again, select All Suggestions from the filter menu.