Modify foreach loop for social sharing links?

Your issue has nothing to do with the foreach. The problem is this part:

implode( '&', $social_link['query'] )

implode() only connects the values. There’s nothing in this code that adds the keys or an =.

If you want to add an array of key/values as a query string to a URL, WordPress provides a function for this called add_query_arg(), it accepts an array of key values and a URL to add them to.

In your case you’d use it like this:

<a target="_blank" href="https://wordpress.stackexchange.com/questions/295504/<?php echo esc_url( add_query_arg( $social_link["query'], $social_link['base'] ) ); ?>">
    <?php echo $social_link['title']; ?>
</a>

Note my use of esc_url. As the documentation states:

Important: The return value of add_query_arg() is not escaped by default. Output should be late-escaped with esc_url() or similar to help prevent vulnerability to cross-site scripting (XSS) attacks.

Another thing to consider is that the values in the query string need to be URL encoded. You can do this with the urlencode() PHP function:

'title' => urlencode( get_the_title() ),

However you’ll need to do this for every value if you do it like that. A way do to this with less code would be to use array_map() to apply urlencode() to every value just before putting into add_query_arg():

foreach( $social_links as $social_link ) :
    $query_args = array_map( 'urlencode', $social_link['query'] );
    ?>

    <li>
        <a target="_blank" href="https://wordpress.stackexchange.com/questions/295504/<?php echo esc_url( add_query_arg( $query_args, $social_link["base'] ) ); ?>">
            <?php echo $social_link['title']; ?>
        </a>
    </li>

    <?php
endforeach;