How to use get_the_terms() to display multiple terms?

I’m going to go and test this somewhere so I may need to make edits, but I think this should do it for you… as Michael mentioned in the comments, you have to wrap the output in the foreach. The method below will place a comma after each one, so I wrap the separator commas in their own span and then use CSS to hide the last one.

$sources = get_the_terms( $post->ID, 'source' );
if( !empty( $sources ) && !is_wp_error( $sources ) ) {
    echo '<span class="source-meta">';
    foreach( $sources as $source ) {
        $source_link = sprintf(
            '<a href="https://wordpress.stackexchange.com/questions/364187/%1$s">%2$s</a>%3$s',
            esc_url( get_term_link( $source ) ),
            esc_html( $source->name ),
            '<span class="sep">, </span>'
        ); 
        echo sprintf( esc_html__( '%s', 'textdomain' ), $source_link );   
    }
    echo '</span>';
}

In your stylesheet (style.css) you then want the following:

.source-meta .sep:last-of-type{
     display:none;
}