### Godot version

v4.1.stable.official [970459615]

### System information

Windows 10

### Issue description

When changing the `file_mode` of `FileDialog` from "Open File" to "Save File" via code the "Save" button keeps disabled until a file or folder is selected if the "Open" button was disabled before.

Basically the button activity has to be updated when `file_mode` is changed. I have made the change already but the last time I opened an PR without an issue some people requested I open one. So here you are!

### Steps to reproduce

- Open the MRP and start it
- click anywere to open the dialog
- after 10 seconds the dialog changes file_mode
- if the button is disabled before the change it is as well after it

### Minimal reproduction project

[file_dialogue_test.zip](https://github.com/godotengine/godot/files/11991311/file_dialogue_test.zip)

ERR_FAIL_COND(p_event.is_null());
	Ref<InputEventKey> k = p_event;
	if (k.is_valid() && has_focus()) {
		if (k->is_pressed()) {
			bool handled = true;
			switch (k->get_keycode()) {
				case Key::H: {
					if (k->is_command_or_control_pressed()) {
						set_show_hidden_files(!show_hidden_files);
					} else {
						handled = false;
					}
				} break;
				case Key::F5: {
					invalidate();
				} break;
				case Key::BACKSPACE: {
					_dir_submitted("..");
				} break;
				default: {
					handled = false;
				}
			}
			if (handled) {
				set_input_as_handled();
			}
		}
	}
}
void FileDialog::set_enable_multiple_selection(bool p_enable) {