Bulk updating PostgreSQL table using lookup in ano

I'm keeping track of the unique combinations encountered of three different integer IDs using the solution described in Continuously insert all unique combinations encountered of three IDs. These IDs are a combination of product/group/region IDs etc.

Now I want to bulk update another table by finding the unique IDs that correspond to those combinations. I'm trying to do that using the function update_with_combination_ids below, but it doesn't work because Postgres has limited support for multi-dimensional arrays. In particular, I'm struggling with implementing WHERE ARRAY[comb.some_id1, comb.some_id2, comb.some_id3] IN (p_combinations[i]) because I can't properly pass an integer[][][] argument to the Postgres function.

I could implement it as many individual update statements passed as one transaction, but that seems suboptimal from a performance perspective. Ideally, I would love to do this without needing a for-loop, but just having a single function for bulk updating would be a good start.

How do I implement this bulk update?

CREATE TABLE combinations (
    id serial PRIMARY KEY,
    some_id1 integer NOT NULL,
    some_id2 integer NOT NULL,
    some_id3 integer NOT NULL
);
CREATE UNIQUE INDEX ON combinations(some_id1, some_id2, some_id3);

CREATE OR REPLACE FUNCTION unnest_2d_1d(ANYARRAY, OUT a ANYARRAY)
  RETURNS SETOF ANYARRAY AS
$func$
BEGIN
   FOREACH a SLICE 1 IN ARRAY $1 LOOP
      RETURN NEXT;
   END LOOP;
END
$func$  LANGUAGE plpgsql IMMUTABLE;

CREATE OR REPLACE function create_combinations_if_needed(p_combinations integer[][]) RETURNS boolean
LANGUAGE sql AS
$$
   INSERT INTO combinations (some_id1, some_id2, some_id3)
   SELECT unnest[1], unnest[2], unnest[3]
   FROM unnest_2d_1d(p_combinations) AS unnest
   ON CONFLICT (some_id1, some_id2, some_id3)
   DO NOTHING
   RETURNING TRUE;
$$;

SELECT * FROM create_combinations_if_needed('{{1, 10, 100}, {2, 11, 101}}'::integer[]);


CREATE OR REPLACE FUNCTION update_with_combination_ids(p_row_ids integer[], p_combinations integer[][][]) RETURNS boolean
LANGUAGE plpgsql AS
$$

   BEGIN     
       -- Find the combination IDs in combinations table and and save them into this table
       FOR i in 1..array_length(p_row_ids, 1) LOOP
           UPDATE user_info
           SET combination_ids = matched_combinations.ids
           FROM
               (
               SELECT ARRAY_AGG(mc.id ORDER BY mc.id) AS ids
               FROM combinations comb
               WHERE ARRAY[comb.some_id1, comb.some_id2, comb.some_id3] IN (p_combinations[i])
               ) AS matched_combinations
           WHERE user_info.id = p_row_ids[i];
       END LOOP;
       RETURN TRUE;
   END;
$$;