I've verified what I described in post above with the following settings..
- System preferences > desktop & dock > scroll down to "displays have separate spaces" and turn that on
- System preferences > desktop & dock > stage manager > turn on > customize > turn on "recent items"
- In dock, right-click on each app you plan to run. Select "options" > "assign to" > "none"
...and with the following actions taken:
- I launched notes, messages and safari on virtual desktop 1 and made sure none were full screen, and none of the windows were all the way to the left side of the monitor -- otherwise the app icons don't show (unless you're careful to click right at the left edge of the monitor, which is a hassle)
- I went to virtual desktop 2 and launched word, excel, and preview, same attention to window location
- I went to virtual desktop 3 and launched pages and keynote, same attention to window location
With settings and actions above -- and with more than one application running in each virtual desktop -- stage manager operates and auto-hides apps as I switch between them, and it does that on each virtual desktop.