@popey Huh. I guess it's not very intuitive. The only way I've discovered is:
From the main menu, choose "Tetra Channel."
Type in my username in the search bar.
Click the "Heart" in the popup profile that appears?
(Not sure why that functionality isn't present in the full profile view. Maybe I'll open an issue https://github.com/tetrio/issues/issues?q=is%3Aissue+is%3Aopen+add+friend)