Showing all users who match 2 meta fields with current user

You’re very close.

First, make sure you’re using unique variable names. I have set $current_seeking_id for the meta key seeking_first and $current_team_id for the meta key team_manager.

Next, you have to use these in your query to match. I’ve placed these variables at the value for your meta_query.

This assumes that the seeking_first value matches the person_talent value and the team_manager value matches the team_number value. This may not be the case and you may have to do some additional work for these to match.

$current_user_id = get_current_user_id();
$current_seeking_id = get_user_meta( $current_user_id, 'seeking_first', true );
$current_team_id = get_user_meta( $current_user_id, 'team_manager', true );
$args = array(
    'meta_query' => array(
        'relation' => 'AND',
        array(
            'key' => 'person_talent',
            'value' => $current_seeking_id,
            'compare' => '='
        ),
        array(
            'key' => 'team_number',
            'value' => $current_team_id,
            'compare' => '='
        )
    )
);

$user_query = new WP_User_Query( $args );

$results = $user_query->get_results();
if ( ! empty( $results ) ) {
    echo '<ul>';
    foreach ( $results as $user ) {
        echo '<li>' . $user->first_name . ' - ' . $user->user_email . '</li>';
    }
    echo '</ul>';
} else {
    echo 'No users found.';
}

Note: I also cleaned up the query result to set a variable for the get_results so as to only call this once. See $results = $user_query->get_results();