Using my desktop PC:
If I hover my pointer over a topic button, I get a drop-down balloon that gives me the option to “Add Topic”.
This happens regardless of where the button is located: a question, another user’s profile, or the “Popular topics” block on each section page.
If one wants to add a topic that doesn’t exist, I guess one could create a question and include that topic, and add it from there.
However, I don’t see any way to add a topic on my profile’s Topics page.
I.e., there’s no link nor are there any directions to add one on that page, that I can see.