What is the correct workflow for modifying child themes?

What you are doing is correct. Any changes like the ones you are doing should go into a child theme or a custom plugin. Since we are talking about CSS, which is very theme specific, changes should go into a child theme

EDIT

From comments, and credit to @birgire,

(styles are) sometimes handled by the theme itself via the theme customiser or theme options

To answer the other comment, the dev tools on browsers are excellent tools to inspect elements in order to know how that specific element is displayed. This will not only tell you the specific color/font size etc the element is using, but also the HTML tag which wraps that element and the particular class/id of that specific tag

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