I've tried the obvious intuitive way: click the text block and then click the Character Style from the Assets panel. Does nothing. I've also tried selecting all the text then clicking the Character Style from the Assets panel. Also nothing.
Am I missing something here?
I had already seen that video. I watched it again. It didn't help.
I did, however, figure it out. In the assets panel it was using "list view" by default. The videos I've seen all use "grid view". I assumed this would make no difference since they're after all just "views". But, after switching to grid view, I can now do what I was describing in the OP. When I switch back to list view it doesn't work.
This seems to be a bug since I can't imagine this being intended behavior.
The hit area is a little smaller in list view, though it's something we're looking at changing. You can click on the character style's preview (not the text) to apply it while in list view.
If the text is grouped it won't apply the character style