How can I check whether a number is contained in comma separated list stored in a varchar column?

You should really redesign this table to split out those values from being comma separated to being in individual rows. However, if this is not possible, you are stuck with doing string comparison instead:

DECLARE @id INT = 3
DECLARE @stringId VARCHAR(50) = CAST(@id AS VARCHAR(50))

SELECT * 
FROM MyTable 
WHERE categoryIds = @stringId -- When there is only 1 id in the table
OR categoryIds LIKE @stringId + ',%' -- When the id is the first one
OR categoryIds LIKE '%,' + @stringId + ',%' -- When the id is in the middle
OR categoryIds LIKE '%,' + @stringId -- When the id is at the end

SELECT * 
FROM myTable 
WHERE (',' + RTRIM(categoryIds) + ',') LIKE '%,' + @stringId + ',%'

Here @stringId is your text to be searched. In this way you can avoid unnecessary multiple where conditions

Kind Regards, Raghu.M.