PopupMenu in plugin grabs keyboard events

When I use a PopupMenu in a plugin, when it is open key-presses in the host don’t work (tested with Logic 10.7.7 running in Rosetta on macOS 12.5 on M2 MBA).

It makes sense for keys like up and down which navigate the menu, but it also happens with other keys (for example “A”).

Is there a way to make all or some of the keys being handled by the host instead of the popup menu? Some users may expect the space bar to start and stop playback at all times…