iPhone Backups

I had an iPhone for my old job.

I had a Samsung for my personal phone.

After quitting that job, I lost my old phone but backed everything up onto my iCloud.

I shortly after switched my personal phone to an iPhone.

After signing into my new phone with my Apple ID, it did not transfer any of my encrypted data and only about 1/3 of my contacts.

I've tried using multiple Q&As on how to access my iCloud backups to get access to my contacts, but the only option it will show for me to perform is to delete my backup from the work phone. How to I actually access the data within the backup?