I'm also experiencing this issue both in mv3. Currently migrating to mv3. I'm using _execute_action in mv3 as it seems to have replaced
_execute_browser_action from mv2.
However, it seems that the suggested keys in the manifest are not being used by Chrome at all. They show up as the set keys in the keyboard shortcuts on the extensions page, but they do not work in practice. To get a shortcut to work, I have to manually override it by literally clicking the edit pencil on the extension shortcuts page, set it (to the exact same key combination as in the manifest), reload the extension, THEN it works! So, while the extension keyboard shortcuts page is recognising the shortcut from the manifest (and filling it into the shortcut box for my extension), the browser is not recognising it otherwise - unless I override it manually in on the shortcuts page.