PostgreSQL Window Function: How to reference a column from the current row vs. a column from the frame row?

Question

[db<>fiddle link]

I have the following data, by group, each row having an increasing index, and containing a limit and a value:

CREATE TABLE items ("group" VARCHAR, index INTEGER, "limit" INTEGER, value INTEGER) ;

INSERT INTO items ("group", index, "limit", value) VALUES 
  ('A', 1, 2, 1), ('A', 2, NULL, 3), 
  ('B', 1, 3, 2), ('B', 2, NULL, 2), ('B', 3, 1, 3), ('B', 4, 2, 5), 
  ('C', 1, 2, 3), ('C', 2, 2, 3), ('C', 3, NULL, 4), ('C', 4, 5, 5) ;

 group | index | limit | value 
-------+-------+-------+-------
 A     |     1 |     2 |     1
 A     |     2 |       |     3
 B     |     1 |     3 |     2
 B     |     2 |       |     2
 B     |     3 |     1 |     3
 B     |     4 |     2 |     5
 C     |     1 |     2 |     3
 C     |     2 |     2 |     3
 C     |     3 |       |     4
 C     |     4 |     5 |     5

For each row, I want to know the next index from the same group whose value is stricly above the limit of the current row, i.e.:

 group | index | limit | value | next
-------+-------+-------+-------+------
 A     |     1 |     2 |     1 |    2
 A     |     2 |       |     3 |     
 B     |     1 |     3 |     2 |    4
 B     |     2 |       |     2 |    
 B     |     3 |     1 |     3 |    4
 B     |     4 |     2 |     5 |    
 C     |     1 |     2 |     3 |    4
 C     |     2 |     2 |     1 |    4
 C     |     3 |       |     1 |    
 C     |     4 |     5 |     5 |    

Question: how to achieve this with window functions? I thought about the following query, but I do not know how to specify in my CASE that limit refers to the current row while value refers to the frame row:

SELECT *,
       MIN(CASE WHEN value < "limit" THEN index ELSE NULL END) 
              OVER (PARTITION by "group" ROWS BETWEEN 1 FOLLOWING AND UNBOUNDED FOLLOWING) AS next
FROM items

Thanks in advance for any help!