How to trigger widget re-render while plugin UI is open?

Plugin and Widget API Questions
1

Here’s my widget:

function MyWidget() {
  const [input, setInput] = useSyncedState('myInput', '')
  usePropertyMenu(
    [
      {
        itemType: 'action',
        tooltip: 'Open Plugin UI',
        propertyName: 'open-plugin-ui',
      },
    ],
    ({ propertyName, propertyValue }) => {
      switch (propertyName) {
        case 'open-plugin-ui':
          return new Promise(() => figma.showUI(__html__));
      }
    },
  );
  useEffect(() => {
    console.log('re-render:', input)
  })
  return (
    <Input
      value={input}
      onTextEditEnd={(e) => setInput(e.characters)}
    />
  )
}

While plugin UI is open, no matter how I change my input state, the widget won’t re-render.