A nested INSERT, UPDATE, DELETE, or MERGE statement must have an OUTPUT clause in UPDATE

I'm trying to update some values based on every Id in the list. The logic I have seems to be what I want.

I want to populate a temporary table of Ids. Then for every ID I want to apply this query and output the deleted date and the ID into a new table I've created.

I keep getting the error:

Msg 10716, Level 15, State 1, Line 25 A nested INSERT, UPDATE, DELETE, or MERGE statement must have an OUTPUT clause.

What does this mean? I thought I am OUTPUTTING into the new table I've created.

USE datatemp

GO


DECLARE @idlist TABLE (id INT)
INSERT INTO @idlist (id) VALUES (3009099)

DECLARE @EndDate DATETIME
SET @EndDate = '2099-12-12'

IF NOT EXISTS (SELECT 1 FROM INFORMATION_SCHEMA.TABLES WHERE TABLE_NAME = 'TEMP_TABLE')
BEGIN
    CREATE TABLE  [TEMP_TABLE] (     
        [id] INT,
        [thedatetoend] DATETIME); 
END

BEGIN TRY
    SELECT  *
    FROM @idlist AS idlist
        OUTER APPLY(
                    UPDATE [custprofile]
                    SET thedatetoend = @EndDate
                    OUTPUT idlist.id, DELETED.thedatetoend
                        INTO [TEMP_TABLE]
                    FROM [custprofile] as bc
                    INNER JOIN [custinformation] as cc
                    ON cc.custengageid = bc.custengageid
                    WHERE cc.id = idlist.id
                                    AND bc.modifierid = 2
                                    AND bc.thedatetoend > GETDATE()
                                    AND cc.type = 1) o