If I understand your question correctly you are copying
mod_articles_news to create a new module called '
mod_my_new_module and in the
mod_my_new_module.xml you leave the
<languages> settings the same as you have pasted in your question above? And the problem is when you install your new Module the MOD_TEXT_STRING doesn't get translated?
<language> elements of the .xml file are only used during installation to tell the installer where to the find the language files(.ini & .sys.ini) you have provided in your installation file(.zip file) so that they can be copied to the Language folders of the Joomla instance. If you aren't providing any language files then the above two statements should be producing an error on installation they can't be found.
When your Module is called the processing tries to automatically resolve the name of your language files, expecting them to be called
mod_my_new_module.sys.ini and because you haven't supplied during installation any that they are not found.
You need to copy/create your own language files using the naming conventions outlined in the documentation and include them when you install your new module.
You could force the module to load the language files for
mod_articles_news but if you follow the normal process then it isn't required.
If you want to just copy the files and rename them to match your new module name in the Language directory and then can continue to use Discover to find them that is quickest approach.
However if you want to learn how to create a module 'properly' then read some of the tutorials on creating modules and extension manifest & language files as you will find it more useful than relying on Discover.