VMX I don't think the widget would work here. I'm talking about the Android search intent - which things like the global android search context menu use. My guess is the widget is hard coded (patching the Google app would be required). I don't use the Google app or it's widgets at all. I also don't use Google's official launcher - I use Nova.
I'm in the US (using a Pixel 8 with latest Android, stock). That being said, this has been a feature for years (it uses the old menu to select the search provider, I wouldn't doubt it's from Honeycomb). Both Firefox and the Tor Firefox browser declare their ability to handle searching. So this isn't related to the EU anti-gatekeeping law.
