Forgot to update the thread with the solution I found:
Created user with home dir
sudo useradd <user>
sudo passwd <pass>
added to sudoers
sudo usermod <user> -aG sudo
sudo vi /etc/sudoers
created their ssh folder
sudo mkdir /home/<user>/.ssh
generated keys with the new user
ssh-keygen -t ed25519
created authorized_keys file in .ssh and copied pub key
sudo vi /home/<user>/.ssh/authorized_keys
changed ownership of file and group to new users
sudo chown <user>:<group> authorized_keys
Created AZ key vault secret via AZ CLI
Created local file with private key values
Uploaded file to AZ CLI
az keyvault secret set --vault-name <vault_name> --name <secret_name> --file <file_name>