permalinks - Custom optional parameter in page URL

I'm losing my mind, so I do hope I can get some help here..

What I'm trying to do is to create an optional parameter for search page, just for the sake of SEO

For example, there are the options:

/search/ (category = null)

/search/contracts (category = contracts)

/search/.../ (category = whatever this parameter $1 is)

While search is a page

I've tried adding htaccess rewrite rule, and wordpress simply redirected 301 without passing the parameter. Then I tried with add_rewrite_endpoint, nothing worked whatsoever and I've tried with

function wpd_add_query_vars( $qvars ) {
  $qvars[] = 'category';
  return $qvars;
}
add_filter( 'query_vars', 'wpd_add_query_vars' );

add_rewrite_rule(
    '^search/([^/]+)/?',
    'index.php?post_id=806&category=$matches[1]',
    'top'
);

add_rewrite_tag('%category%', '([^&]+)');

flush_rewrite_rules();

Do note I tried just about every permutation, also tried plugins, nothing worked. It was either a 404 or the $wp_query->query_vars did not include the parameter.

Thanks in advance..