"Type To Siri"

Here's an updated version of the AppleScript that will run on Big Sur:

tell application "System Events" to tell the front menu bar of process "SystemUIServer"
	tell (first menu bar item whose description is "Siri")
		perform action "AXPress"
	end tell
end tell

delay 1

tell application "System Events" to tell the process "NotificationCenter"
	set notifyWindows to every window
	repeat with notifyWindow in notifyWindows
		if description of notifyWindow is "system dialog" then
			set elements to entire contents of notifyWindow
			tell (first text field of first group of first UI element of first scroll area of notifyWindow)
				set focused to true
				set value to ASTypeToSiriQuery
				perform action "AXConfirm"
			end tell
			exit repeat
		end if
	end repeat
end tell

Edit: I should mention, I'm not very good with AppleScript, so this is probably going to break in the future, but it works for now.