Describe the request

It would be handy if the quick selection menu would also display (in the overlay) if we are selecting a board from "board manager" core or the sketchbook one.

Screenshot attached

Describe the current behavior

Only the platform name is displayed.

Arduino IDE version

2.2.1

Operating system

Linux

Operating system version

Arch

Additional context

No response

Issue checklist

• I searched for previous requests in the issue tracker
• I verified the feature was still missing when using the latest nightly build
• My request contains all necessary details