How to remove comment count column in Posts inside the admin dashboard?

Should be work, if you use the filter manage_posts_columns.
The hook is fine, see https://core.trac.wordpress.org/browser/tags/5.8/src/wp-admin/includes/class-wp-posts-list-table.php#L714

Documentation include examples – https://developer.wordpress.org/reference/hooks/manage_posts_columns/

Example:

function remove_posts_columns( $columns, 'post' ) {

    unset( $columns['comments'] );
    return $columns;
}
add_filter( 'manage_posts_columns',  'remove_posts_columns', 10, 2 );