Statement-level Triggers

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Page: https://www.postgresql.org/docs/11/sql-createtrigger.html
Description:

The AFTER Statement-level Trigger runs into infinite execution when another
set of rows are affected for the same table through this trigger. Consider
this use case where a table storage_locations that manages a hierarchy of
storage_locations in stores, and thus having following columns (for
simplicity):
storage_location_id                 SERIAL               NOT NULL
PRIMARY KEY,
store_id                                   INTEGER            NOT NULL,
-- REFERENCES stores
storage_location_nm               VARCHAR (25)   NOT NULL,
parent_storage_location_id     INTEGER                    NULL
REFERENCES   storage_locations,    ---- NULL for root storage locations
storage_location_path             TEXT                  NOT NULL
I have a BEFORE ROW trigger, which updates the storage_location_path with
parent's storage_location_path, if any, concatenated with its
storage_location_name. This works fine - no issues.

I have another AFTER UPDATE STATEMENT-level Trigger and function definitions
as below (which updates the storage_path of the children):
CREATE FUNCTION TRG_storage_locations_b_u_AS_DML ()
    RETURNS    TRIGGER
AS    $$
DECLARE
    v_separator    VARCHAR (1)        =    '/';
    v_cnt        INT;
BEGIN
                                       -- [ -- Required to prevent infinite
recursion
    SELECT    COUNT (*)
        INTO    v_cnt
    FROM    new_table;

    IF (v_cnt > 0) THEN
                                       -- ] -- Required to prevent infinite
recursion
        UPDATE    storage_locations
            SET     storage_location_path    =    COALESCE (i.storage_location_path ||
v_separator, '') || storage_locations.storage_location_nm
        FROM    inserted    i
            JOIN    deleted    d
                ON    (    i.storage_location_id    =    d.storage_location_id
                    AND    i.storage_location_path    !=    d.storage_location_path
                    )
        WHERE    storage_locations.parent_storage_location_id    =    i.storage_location_id;
    END IF;
    RETURN NULL;
END
$$ LANGUAGE plpgsql;

CREATE TRIGGER storage_locations_b_u_AS_DML
    AFTER    UPDATE
        ON    storage_locations
            REFERENCING    NEW    TABLE    AS    inserted
                        OLD    TABLE    AS    deleted
        FOR    EACH STATEMENT    EXECUTE    FUNCTION    TRG_storage_locations_b_u_AS_DML ();

Notice that the Trigger is getting called endlessly (if the number of rows
in the NEW TABLE are NOT checked). I reckon if there are not any rows, what
is the need to call the trigger. Or, may be, I am missing something, which I
need to learn.