Query to get ids of entries which appear in arbitrary amount different lists

I have this kind of data presented to me. For my query I'm given a list of category ids.
Let's say I'm given three lists with

1. {93, 94}
2. {88, 87, 86}
3. {93}

Now I would need a query, which would give me product ids, which appear at least once in ALL of those lists and for which the status is 1. So for the example query the result should be:

This should work for SQL Server 2016 and above.

CREATE TABLE table1
(
id INT,
category_id INT,
product_id INT,
status INT
)

INSERT INTO table1
    (id, category_id, product_id, status)
VALUES
    ( 13, 93, 2137, 1)
    ,( 14, 94, 2137, 1)
    ,( 15, 93, 2138, 2)
    ,( 16, 94, 2138, 2)
    ,( 17, 87, 2128, 1)
    ,( 18, 94, 2128, 1)
    ,( 19, 87, 2139, 2)
    ,( 20, 94, 2139, 2)
    ,( 21, 88, 2132, 1)
    ,( 22, 93, 2132, 1)
    ,( 23, 88, 2140, 2)
    ,( 24, 93, 2140, 2)
    ,( 25, 87, 2137, 1)
    ,( 26, 87, 2141, 2)
    ,( 27, 93, 2136, 1)
    ,( 28, 93, 2137, 1)
    ,( 29, 88, 2134, 1)
    ,( 30, 88, 2143, 2)

CREATE TABLE Input 
    (IdLst varchar(100))
INSERT INTO Input (IdLst)
VALUES 
    ('{93, 94}')
    ,('{88, 87, 86}')
    ,('{93}')

;WITH Categories AS (
    SELECT CONVERT(INT, Value ) category_id
    FROM Input 
    CROSS APPLY STRING_SPLIT(REPLACE(REPLACE( IdLst, '{', ''), '}', ''), ',')
)
SELECT product_id
FROM Categories
INNER JOIN table1 ON table1.category_id = Categories.category_id
GROUP BY product_id
HAVING COUNT(1) = (SELECT COUNT(1) cntCategories FROM Categories )

The first step in any solution is to normalize the selection criteria data into a table of the form { category_group_id, category_id } with only one category_id for row. There are several ways to do this but I've used the relatively new STRING_SPLIT function here (same as Luis LL). This normalized criteria may be loaded into a temp table or included as a Common Table Expression (CTE) as is done below.

Once the criteria is normalized, the real problem can be solved by (1) filtering the input data by status, (2) joining it with the normalized selection criteria from above, (3) grouping by product ID, and then (4) counting the number of distinct category group IDs matched. If that count matches the total number of category group IDs (three for the sample data), we have a match.

;WITH NormalizedCategoryIds AS (
    SELECT C.category_group_id, CAST(S.Value AS INT) AS category_id
    FROM CategoryIds C
    CROSS APPLY STRING_SPLIT(
        REPLACE(REPLACE(category_id_list, '{', ''), '}', ''),
        ',') S
)
SELECT D.product_id
FROM SampleData D
JOIN NormalizedCategoryIds C on C.category_id = D.category_id
WHERE D.status = 1
GROUP BY D.product_id
HAVING COUNT(DISTINCT C.category_group_id) = (SELECT COUNT(*) FROM CategoryIds)

If we started with criteria that was already normalized, the HAVING clause could be changed to:

HAVING COUNT(DISTINCT C.category_group_id)
    = (SELECT COUNT(DISTINCT C2.category_group_id) FROM NormalizedCategoryIds C2)

That value could also be calculated ahead of the query.

Sample results:

Even though not in the original posted results, 2132 is also included here, because it matches all three category groups. The 93 row matches category groups 1 and 3 and the 88 record matches category group 2.

See this db<>fiddle for a working demo including some extra test data.