As far as I know Polylang and Loco Translate also worked fine with it.
Adding support for translation plugins can be quiet time consuming, so it’s not always possible to make it work with all of them.
I understand, but I would rather have the plugin just supporting PO/MO files as was intended by WordPress.
Then please explain how. I want the words in store-listings-below.php to be multilangual and right now I can only translate them into 1 language through the WP admin.
The article that I linked to clearly explains how to create different language files.
The label texts however are a special case since they are stored in the database to keep them easy to edit in the admin panel itself, so this does create an issue with multiple languages.
For those field you will need to use a multilingual plugin, or edit the template and add replace the current labels with something like this, and then generate a custom language file ( name it your-translation-de_DE.po for German based on the text below ) for it.
$output .= "\t\t\t\t\t" . '<label for="wpsl-radius-dropdown">' . __( 'Search radius', 'your-translation' ) . '</label>' . "\r\n";
But the easy solution is to simply use a multilingual plugin.
I am using Sublanguage, so indeed I have to edit core files. Too bad….