Statement-level trigger results in recursion

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.

Thanks,

Jiten