If you’ve lost the private key, you can still recover data using the EBS volume method:

Steps:
Stop the affected EC2 instance
Go to EC2 → Volumes (EBS)
Detach the root volume from the instance
Attach this volume to another EC2 instance (that you can access) as a secondary disk
Log in to the new instance
Mount the attached volume and access the data
Copy the required files or create a backup