### 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)

}
	}
}
void FileDialog::_cancel_pressed() {
	file->set_text("");
	invalidate();
	hide();
}
bool FileDialog::_is_open_should_be_disabled() {
	if (mode == FILE_MODE_OPEN_ANY || mode == FILE_MODE_SAVE_FILE) {
		return false;
	}
	TreeItem *ti = tree->get_next_selected(tree->get_root());
	while (ti) {
		TreeItem *prev_ti = ti;
		ti = tree->get_next_selected(tree->get_root());
		if (ti == prev_ti) {
			break;
		}
	}
	
	if (!ti) {
		return mode != FILE_MODE_OPEN_DIR; 
	}
	Dictionary d = ti->get_metadata(0);
	
	return ((mode == FILE_MODE_OPEN_FILE || mode == FILE_MODE_OPEN_FILES) && d["dir"]) || 
			(mode == FILE_MODE_OPEN_DIR && !d["dir"]);
}
void FileDialog::_go_up() {