list of tags overlay

Notice that the strip_tags() will remove all HTML tags.

If you want to allow <br>, then you can add it as the second input parameter:

echo strip_tags( $text, '<br>' );

I want to display them like a list

For that case, you could try this example:

<p class="nom">
    <ul>
        <?php the_terms( get_the_ID(), 'project_tag', '<li>', '</li><li>', '</li>' ); ?>
    </ul>
</p>

where the_terms() uses the get_the_term_list().

Update:

Here’s how you could replace the commas (,) with <br>:

<p class="nom">
    <?php 
         $tmp = get_the_term_list( get_the_ID(), 'project_tag', '', '<br>', '' );
         echo strip_tags( $tmp, '<br>' );  
    ?>
</p>

but regarding the <ul> list I think it’s an CSS issue.