Update large table with millions of rows in Azure SQL Server, in Parallel
Why not update the table with a single UPDATE statement?
If your database is set to READ COMMITTED SNAPSHOT and you can afford to block other sessions from writing to the table during the update, that's the simplest option.
Otherwise update them sequentially in batches (option 2).  Running lots of parallel DML statements (Option 1) is too complicated and too prone to blocking and deadlocking issues.  IE it's not going to solve all the problems of using a single UPDATE statement, and it introduces new ones.