Hard Drive Erased Whilst Accepting to use it as Backup

Lesson learned the hard way

Data Recovery may Depend on if the External Drive is a Mechanical Drive or SSD drive

If you intended to try and recovery the Data - Immediately Stop using the drive

The more new data written to the drive the less chances of recovery any data

You will need to search for a Reputation Professional Data Recovery Company

No, I do not know or can I recommend any companies just because I use a Single Drive for a Single Purpose - Time Machine Backups

They will tell you, the probably can recovery Some Data but Not ALL Data

Caveat If the drive is an SSD Drive - forget the idea of Data Recovery

Connect a storage device to your Mac

Connect an external storage device, such as a USB drive or Thunderbolt drive, to the appropriate port on your Mac. Identify the ports on your Mac.

• Use a storage device with at least twice the storage capacity of your Mac. For example, if your Mac has 1TB of storage, your backup disk should ideally have at least 2TB of storage. If Time Machine needs more storage space, your Mac will let you know.
• Use your Time Machine backup disk only for Time Machine backups, not for storage of other files.*

Follow on

For future purposes

To truly protect your non replaceable Data

Have a 3-2-1 Rescue Plan in place and always current

3 Backups using 2 methods and 1 off site incase of natural disaster or un-natural disaster.

Each of the above should be done to a Dedicated Single Purposed External Drive 

Below link is intended to augment what TM Backup does 

https://bombich.com