SQL Insert multiple values with UNIQUE constraint
SQL constraint violation affects the entire statement, you cannot ignore individual rows.

What you can do is insert only the rows that don't violate the constraint. There are several ways to do that, for example

INSERT INTO dzp.contractid(vnr)
SELECT DISTINCT vnr FROM dzp.accounts_stage s 
WHERE NOT EXISTS (SELECT 1 FROM dzp.contractid WHERE vnr = s.vnr)


You could also use MERGE:

MERGE dzp.contractid AS t
USING dzp.accounts_stage AS s
ON (t.vnr = s.vnr) 
WHEN NOT MATCHED BY TARGET 
THEN INSERT(vnr) VALUES(s.vnr)