I'm probably still missing something, but my interpretation is that the rules are:
1) No number exist in VWNUMBERS => return NULL.
2) At least one number exist in the table, but it is Conflicting => return 0.
3) At least one number exist in the table and is Valid => return 1.
This leads to small modification of my query above, replace MAX with MIN:
CREATE OR ALTER PROCEDURE Vamshi_sp @list nvarchar(MAX) AS
; WITH CTE AS (
SELECT COUNT (DISTINCT WN.APPKEY) AS appkeycnt
FROM dbo.VW_NUMBER WN
WHERE WN.ANUMBER IN (SELECT value FROM string_split(@list, ','))
AND WN.UNITKEY IN (SELECT IC.UNITKEY FROM dbo.VW_DATA IC WHERE IC.UNITNAME = 'MAS')
GROUP BY WN.DEPTKEY, WN.ANUMBER
), CTE2 AS (
SELECT MIN(appkeycnt) AS mincnt FROM CTE
)
SELECT CASE WHEN mincnt IS NULL THEN NULL
WHEN mincnt = 1 THEN 1
ELSE 0
END, mincnt
FROM CTE2
go
EXEC Vamshi_sp 'GNW0060077,0456618'
EXEC Vamshi_sp 'NGL0300008,235493'
EXEC Vamshi_sp 'UY1233,VAMPQ34'
EXEC Vamshi_sp 'GNW0060077,0456618,NGL0300008,235493,UY1233,VAMPQ34'
EXEC Vamshi_sp 'GNW0060077,UY1233,NGL0300008'
(I packaged this in a stored procedure to make it easier to run all test cases. Just extract the query and replace the call to string_split with your list of values.)