Start a new theme from scratch to see if you have the same result. I test with theses files and the translation works
style.css
/*
Theme Name: My Theme
*/
functions.php
<?php
add_action( 'after_setup_theme', 'my_theme_load_theme_textdomain' );
function my_theme_load_theme_textdomain() {
load_theme_textdomain( 'my-theme', get_template_directory() . '/languages' );
}
languages/es_ES.po (file languages/es_ES.mo created with poedit)
msgid "Featured"
msgstr "Destacados"
index.php
<?php
_e( 'Featured', 'my-theme' );