You asked
Where is our data stored?
The short answer
On your own hardware, encrypted, with an encrypted backup you keep off site. There is no cloud account and no outside party that can read it, because only you hold the keys.
The records live on computers your staff can point to, administered by your own IT. The backup is a locked drive you keep somewhere safe, not an account with an outside company.
Encryption at rest is what makes both ends safe: a stolen machine or a lost backup drive holds only unreadable ciphertext without your keys.
Because the records are files on your hardware, they are also yours to export, copy, or move at any time.