[toolbar] Should radio inputs behave differently inside of a toolbar?

Pre-amble: Yes I know APG is not a spec but the aria specification is a bit lacking on details around focus management aside from explaining how activedescendant works.

In the APG radio pattern and also mentioned in passing on the MDN page for the radiogroup role there's mention that radiogroups inside of a toolbar should behave specially.

Specifically they seem to imply that radiogroups inside of a toolbar should NOT have selection follow focus.

1. Is this correct (the logic makes sense)?
2. Should we do something special here in the toolbar implementation for radio inputs?
3. If so what should we do?

I guess the same maybe applies to focusgroup but perhaps is too heavy handed for focusgroup. Though this does seem like a tricky thing to implement manually because you don't know if you're inside of a toolbar role or not easily.

Start by comparing the APG radio pattern and MDN radiogroup keyboard-interaction guidance linked in the issue with the current toolbar and focusgroup behavior. Determine whether toolbar-contained radio groups should suppress selection-on-focus and whether that applies to focusgroup; done means reaching a documented behavior decision and defining the required implementation scope.