Equivalent of url_to_postid() for non-post URLs?

The simplest solution is to get all the existing rewrite rules, match the requested URl to one of them, and then convert it into a query.

Like so:

    //  Get all the rewrite rules
    global $wp_rewrite;

    $url_path = "2020/04/test-post"; // Or "tag/whatever" or "feed/atom" etc

    //  Match the URL against WordPress rewrite rules
    $rewrite_rules = $wp_rewrite->wp_rewrite_rules();
    $matched_rule = false;

    foreach ( $rewrite_rules as $pattern => $query ) {
        if ( preg_match( "#^$pattern#", $url_path, $matches ) ) {
            $matched_rule = $query;
            break;
        }
    }

    //  Replace each occurrence of $matches[N] with the corresponding value
    foreach ( $matches as $key => $value ) {
        $matched_rule = str_replace( "\$matches[{$key}]", $value, $matched_rule );
    }

    //  Turn the query string into a WordPress query
    $query_params = array();
    parse_str(
        parse_url( $matched_rule, PHP_URL_QUERY), 
        $query_params
    );

    //  Construct a new WP_Query object using the extracted query parameters
    $query = new WP_Query($query_params);