>doesn't the redo log fill up?

It's not a redo/undo log. It's more like (simplifying things here) having multiple copies of things and different sessions/connections "see" different sets of data. That's why you need to vacuum the database periodically, to garbage collect old rows that are no long accessible to any sessions/transactions.

See https://devcenter.heroku.com/articles/postgresql-concurrency

>is there enough storage space for that?

You do need to make sure you aren't too close to filling your storage, postgres needs some breathing room for this reason.