Update from staging table with multiple registers repeated

There are an AR table and an AR_STAGE table (samples) like this:

DECLARE @AR AS TABLE (
    Patient VARCHAR(50),
    MRN INT,
    Submission DATETIME,
    Active VARCHAR(5),
    Last_update DATETIME
);
INSERT INTO @AR
VALUES
('Zaczeniuk, Ann',  1338728,    null,   'NEW',  null),
('Zaczeniuk, Ann',  1338728,    null,   'NEW',null),
('Palomino, Joseph',717463, '10/09/2023',   'NEW',  null),
('Palomino, Joseph',717463, '10/09/2023',   'NEW',  null),
('Linares, Irma',   3028394,    null,   'NEW',  null),
('Linares, Irma',   3028394,    null,   'NEW',  null),
('Imbery, Layne',   2910744,    null,   'NEW',  null),
('Imbery, Layne',   2910744,    null,   'NEW',  null);

SELECT *
FROM @ar

AR

AR_STAGE

I need to update my AR table with the information of the AR_STAGE, mapping by MRN. I only need to update the records in AR when Submission is in blank or null and are as date value in AR_STAGE, then changing Active= UPDATED. So, the others must be stay as Active=NEW, even if the AR_STAGE.Submission field has a null/blank value.

DESIRED OUTPUT AR TABLE

I tried this query:

MERGE AR AS Target
USING 
  ( SELECT MRN, Submission, COUNT(*) AS A
  FROM AR_STAGE GROUP BY MRN,Submission )  Source
ON Source.MRN = TARGET.MRN
WHEN MATCHED AND  IsNull(Target.[Submission], '') = ''  THEN
UPDATE SET 
Target.[Submission] = Source.[Submission]
,Target.[Last_update] = CURRENT_TIMESTAMP
,Target.Active="UPDATED"

But it brought a wrong output:

WRONG OUTPUT AR TABLE

Because the last four records should’ve been Active=NEW with Last_update= null. This because there is no change on submission.