I think this might help you.
$Button.connect("pressed", self, "_on_button_pressed")
will become
$Button.pressed.connect(self._on_button_pressed)
To make a signal with additional arguments, you would use the new Callable.bind():
$Button.pressed.connect(self._on_button_pressed.bind("Hello", "World"))
Signals will now have their own class, and therefore their own methods. This includes the ability to emit signals through code:
$Button.pressed.emit()
Disconnect signals:
$Button.pressed.disconnect(self._on_button_pressed)
Get all current connections:
$Button.pressed.get_connections()
Check if the signal is connected:
$Button.pressed.is_connected(self._on_button_pressed)