Update Taxonomy from Values Stored in Relationship Field

Hi, I am studying the documentation of this plugin to see if it can do for me and I must say that the plugin for sure is what I was looking for, but to use it I will need to study more and maybe take advantage of your help.

I’ve created a custom post type “Ricette” and a custom taxonomy “Ingredienti” and I added the taxonomy to the post type “Ricette” using a relationship field, but I figured out that there is no actual relationship between the taxonomy and the recipe:

If I add a new recipe and I select an ingredient from the taxonomy “Ingredienti”, for example garlic, after saving the recipe there is no correlation between the recipe and the taxonomy: If i clic on the taxonomy garlic I don’t see the recipe just made.

After some digging I found this code snippet, but I need some help:
https://docs.pods.io/code-snippets/update-taxonomy-value-stored-relationship-field/

In the example the taxonomy field is pods_genre and is related to the taxonomy genre,
in may case the taxonomy filed is ingredients_relation_field and the taxonomy is ingrediente, so I tried to modify the code like that:

/**
 * Update Taxonomy With Value Of Field Related To A Taxonomy
 * Takes the value of a single- or multi-select field 'pods_genre' related to the taxonomy 'genre' and updates the taxonomy with the term set in the 'pods_genre' field from the custom post type 'films'.
 */
add_action( 'pods_api_post_save_pod_item_films', 'my_tax_update', 10, 3 );
function my_tax_update( $pieces, $is_new_item, $id ) {
    // get the values of the 'pods_genre' field
    $terms = $pieces[ 'fields' ][ 'ingredients_relation_field' ][ 'value' ];
    if ( empty( $terms ) ) {
        // if there is nothing there set $term to null to avoid errors
        $terms = null;
    } else {
        if ( ! is_array($terms) ) {
            // create an array out of the comma separated values
            $terms = explode(',', $terms);
        }
        
        // ensure all values in the array are integer (otherwise the numerical value is taken as a new taxonomy term instead of an ID)
            $terms = array_map('intval', $terms);
    }
    // Set the term for taxonomy 'genre' with $terms
    wp_set_object_terms( $id, $terms, 'ingrediente', false );
    
}

I made an export of the two pods, I thought it might be useful.

{
    "@meta": {
        "version": "2.9.10.2",
        "build": 1671878070
    },
    "settings": {
        "types_only": "0",
        "watch_changed_fields": "0",
        "metadata_integration": "1",
        "metadata_override_get": "0",
        "session_auto_start": "0",
        "wisdom_opt_out": "1"
    },
    "pods": [
        {
            "name": "ingrediente",
            "id": 7,
            "label": "Ingredienti",
            "description": "",
            "type": "taxonomy",
            "storage": "meta",
            "label_singular": "Ingrediente",
            "public": "1",
            "show_ui": "1",
            "hierarchical": "1",
            "rest_enable": "1",
            "_migrated_28": "1",
            "built_in_post_types_ricetta": "1",
            "groups": [
                {
                    "name": "campi_aggiuntivi",
                    "id": 8,
                    "label": "Campi aggiuntivi",
                    "description": "",
                    "weight": 0,
                    "fields": []
                }
            ]
        },
        {
            "name": "ricetta",
            "id": 5,
            "label": "Ricette",
            "description": "",
            "type": "post_type",
            "storage": "meta",
            "label_singular": "Ricetta",
            "public": "1",
            "show_ui": "1",
            "rest_enable": "1",
            "supports_title": "1",
            "supports_editor": "1",
            "_migrated_28": "1",
            "built_in_taxonomies_ingrediente": "1",
            "required": "0",
            "groups": [
                {
                    "name": "campi_aggiuntivi",
                    "id": 6,
                    "label": "Campi aggiuntivi",
                    "description": "",
                    "weight": 0,
                    "fields": [
                        {
                            "name": "ingredients_relation_field",
                            "id": 9,
                            "label": "ingredients_relation_field",
                            "description": "",
                            "weight": 0,
                            "type": "pick",
                            "pick_object": "taxonomy",
                            "pick_val": "ingrediente",
                            "sister_id": "-- Seleziona --",
                            "pick_table": "-- Seleziona --",
                            "required": "0",
                            "pick_format_type": "single",
                            "pick_format_single": "dropdown",
                            "pick_format_multi": "list",
                            "pick_display_format_multi": "default",
                            "pick_display_format_separator": ", ",
                            "pick_allow_add_new": "1",
                            "pick_taggable": "0",
                            "pick_show_icon": "1",
                            "pick_show_edit_link": "1",
                            "pick_show_view_link": "1",
                            "pick_limit": "0",
                            "pick_user_role": "Administrator",
                            "pick_post_status": "publish",
                            "pick_post_author": "0",
                            "repeatable": "0",
                            "repeatable_format": "default",
                            "roles_allowed": "administrator",
                            "rest_pick_response": "array",
                            "rest_pick_depth": "1"
                        }
                    ]
                }
            ]
        }
    ]
}

May be some one can see what I’m doing wrong, thanks in advance.