Sql-server – Dynamically changing an order number to end in _ERR

There is no syntax variant that lets you update the whole row at once. However, there is a shorter form than what you have so far.

Also, you do not actually want to update all columns. The WHERE condition on id pins down at least one column (id) to remain unchanged. But that's just nitpicking.

UPDATE table_a a
SET    (  c1,   c2, ...)
     = (b.c1, b.c2, ...)
FROM   table_b b
WHERE  a.id = b.id;

More details in this related answer:
Bulk update of all columns

DELETE / INSERT

Internally, due to the MVCC model of Postgres, every UPDATE effectively inserts a new row anyway and marks the old one as obsolete. So, behind the curtains there is not much difference between UPDATE and DELETE plus INSERT.
There are some details in favor of the UPDATE route:

• HOT UPDATE.
• TOAST tables: If you have large columns, the content may be stored."out-of-line" in TOAST tables and the new row version can link to the same row in the TOAST table if toasted columns remain unchanged.
• Index maintenance may be cheaper for updates.

Otherwise, locking should be about the same. You need an exclusive lock on affected rows either way. Just make it quick.
If you are dealing with a huge number of rows and you don't need a consistent state (all rows or none), you can split the operation into multiple batches. (Separate transactions!) Increases the total cost, but keeps the lock time per row shorter.

There multiple entry in table patient_encounter for a person_id, so you need to get the person_id with top 1

Try this

update patient_encounter 
Set user_defined4 = 'DTC'
where person_id = (SELECT top 1 person_id from patient_encounter 
                     where  mrkt_plan_id = '489681B4-9D94-413B-95A0-C50D5964F340')

EDIT as per comment, if you are looking to update all the record, use IN as below

update patient_encounter 
    Set user_defined4 = 'DTC'
    where person_id IN (SELECT person_id from patient_encounter 
                         where  mrkt_plan_id = '489681B4-9D94-413B-95A0-C50D5964F340')