OK. Got it for responsive theme actions. That works OK, and eliminates the need for a user agent switcher, which is sweet!
It does expose how a lot of the 3rd party content my site uses is not designed to be automatically responsive, and it still needs to get the general device type in its API parameters to do its complex reformatting.
So this still doesn’t answer what happened to the weaverii_use_mobile function that I used in WeaverII and still need, and is also still coded in the vimeo shortcode in the theme support plugin. I guess what I am saying is that I still need a simple php technique to determine device type, and am not finding that in the tips or forum content.