Recently had an addition put onto my house, new part has a basement which has a sump pump. But doesn’t have a battery backup.
Is it possible to add a backup pump system like this 
? In the same well thing or do I have to replace the whole pump for one like this 
which looks like a 2 in one?
Should be able to add a battery backup.
https://www.secamerica.com/how-to-add-a-battery-backup-to-an-existing-sump-pump/#:~:text=Luckily%2C%20you%20can%20in%20fact,pump%20using%20the%20Pump%20Sentry.
And if you can swing it, I'd honestly throw another small pump in there for redundancy.