How to break a long data migration into multiple transactions?

Question

PostgreSQL

There is a DB where one label occupies a lot of place on a disk.
I added a new column to it.
Now you need to fill it.
Because Since the migration is performed in a transaction and will affect almost all records, it will take a long time and, I assume, the size of the table at the end of the transaction will increase by ~ 2 times (due to MVCC).
That being said, I don't need to perform these changes in a single transaction, but need to perform in a single migration. How to do it?