Steps to reproduce the issue

The language switcher module does not display flags in Joomla 3.9.10 and 4.1. Detailed code pointers below

Expected result

Language switcher on frontend shows flags after following these steps: https://docs.joomla.org/J3.x:Setup_a_Multilingual_Site/Language_Switcher

Actual result

The module shows up, but no language options are shown

System information (as much as possible)

Additional comments

I dug a bit into the code of Joomla 3.9.10 and the culprit seems to be in this snippet:

                         $default = $menu->getDefault($item->lang_code);

			if ($default && $default->language === $item->lang_code)
			{
				$homes[$item->lang_code] = $default;
			}

(see: https://github.com/joomla/joomla-cms/blob/3.10-dev/modules/mod_languages/helper.php#L43 )
on my site, the $default->language is equal to *, probably because the default menu item has language settings 'All'. However '*' is not equal to a language code, e.g. 'en-GB', so no entries are added to the $homes and later down in the helper. php, all language codes are discarder for this reason.

I observed the same behaviour in Joomla 4, but have not debugged the code in that case.