Return a column that displays the last known value (MAX DateTime) from a record table for each row by ID - SQL

I know similar questions have been asked before and I'll include some links at the bottom, but can't work it out for my query.

I want to calculate 2 columns in a view that return the last known status (status A and status B) of a person for each row (status change by DateTime).

I have joined two record tables on date_time that contain information about a persons change in status over time. I want to know the latest value for status A for a person when status B changes and visa versa. For example, when a person's status changes from Hungry to Sad what was their latest (or current) StatusB (Active?).

My current query returns a table:

I want to return a table:

What have I tried?

I've had about 7 attempts at using subqueries and/or joining the table back on it's self to return the value of StatusA_New/StatusB_New at the MAX(DateTime) of the two original tables.

The closest I've go is probably this:

WITH T AS 
(
    SELECT 
        A.DateTime, A.ID, A.StatusA_New
    FROM A
)
SELECT 
    A.DateTime, A.ID, A.StatusA_Old, 
    A.StatusB_New, T.StatusA_New AS StatusA_Current
FROM 
    A
LEFT JOIN 
    T ON (A.DateTime <= T.DateTime) AND (A.ID = T.ID)

Keeping in mind that my current query does not even look at Status changes in B and does not yet deal with the joined DateTime table shown in the example tables.

The joined Table AB uses the following query:

/*example tables*/
create table A
(
    A_DateTime datetime,
    ID varchar(10),
    StatusA_Old varchar(10),
    StatusA_New varchar(10)
)

create table B
(
    B_DateTime datetime,
    ID varchar(10),
    StatusB_Old varchar(10),
    StatusB_New varchar(10)
)

insert into A values
('2021-02-01 23:57:20.000', 1001, NULL, 'Hungry'),
('2021-02-02 23:57:20.000', 1002, NULL, 'Sad'),
('2021-02-03 23:57:20.000', 1001, 'Hungry', 'Happy')

insert into B values
('2021-02-01 23:57:20.000', 1001, NULL, 'Active'),
('2021-02-02 23:57:20.000', 1002, NULL, 'Active'),
('2021-02-04 23:57:20.000', 1002, 'Active', 'Inactive')

SELECT  
     CASE 
        WHEN A.A_DateTime IS NULL THEN B.B_DateTime
        ELSE A.A_DateTime
     END AS DateTime,
     CASE 
        WHEN A.ID IS NULL THEN B.ID
        ELSE A.ID
     END AS ID,
     StatusA_Old, StatusA_New, 
     StatusB_Old, StatusB_New
FROM  
    A
FULL OUTER JOIN 
    B ON A.A_DateTime = B.B_DateTime

Similar questions:

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• Also might relate to this problem (as mentioned by another user) https://www.itprotoday.com/sql-server/last-non-null-puzzle

use a CTE for existing query and then sub-query to get the latest NOT NULL value from the cte

WITH CTE
AS
(
    SELECT  COALESCE(A.A_DateTime, B.B_DateTime)    AS DateTime
        ,COALESCE(A.ID, B.ID)           AS ID
        ,StatusA_Old
        ,StatusA_New
        ,StatusB_Old
        ,StatusB_New
    FROM  A
    FULL OUTER JOIN B
      ON    A.ID        = B.ID
      AND   A.A_DateTime    = B.B_DateTime
)
SELECT  *
    ,(SELECT TOP 1 x.StatusA_New 
        FROM    CTE x 
        WHERE   x.ID = c.ID 
        AND x.DateTime <= c.DateTime 
        AND x.StatusA_New IS NOT NULL 
        ORDER BY x.DateTime DESC) AS StatusA_Current
    ,(SELECT TOP 1 x.StatusB_New 
        FROM    CTE x 
        WHERE   x.ID = c.ID 
        AND x.DateTime <= c.DateTime 
        AND x.StatusB_New IS NOT NULL 
        ORDER BY x.DateTime DESC) AS StatusB_Current
FROM    CTE c
ORDER BY [DateTime]