How to put a class in the p tag automatically added by the_content() in the wordpress loop?

It appears that wpautop(), which adds the <p> tags, doesn’t have any way to filter the <p> tags it adds.

If you’re trying to replace all the <p> tags in the content with your <p class="{...}">, though, you should be able to use the the_content filter:

add_filter( 'the_content', 'wpse412742_class_up_the_paragraphs' );
/**
 * Adds classes to all the <p> tags in the content.
 *
 * @param  string $content The post content.
 * @return string          The post content with the classes added to the <p> tags.
 */
function wpse412742_class_up_the_paragraphs( $content ) {
    $content = str_replace(
        '<p>',
        '<p class="pwp-testmonials-slider__desc_depoimento text-center">',
        $content
    );
    return $content;
}