You can find the keyboard shortcuts for any command by looking through the menus, so if you look in the Format > Formatting menu you will see that “Copy Formatting” has the keyboard shortcut ctrl-opt-cmd-C.
You can add this command to the toolbar by going to View > Customize Toolbar… Add “Copy Style” and “Paste Style” to your toolbar.
I’d found the copy style key combo, but wrongly assumed it would work like Word style painter, and all I had to do was highlght the intended text. When it didn’t change the text style, I thought I was doing something wrong. I didn’t realize that I needed to “paste style”.