I recently came across a “cannot access install” error when deploying from a BitBucket repo Pipeline to WP Engine.
The error occurred on the rsync command, but during debugging I got the same problem with a simple SSH connect. Nothing had changed on either setup recently.
I contacted WP Support and we worked through debugging the problem. We couldn’t find the cause, and so I deleted the SSH key pair from BitBucket, and created a new pair.
I then added the new public key to WP Engine, and everything worked again.
I’m putting this out here in case this helps someone else.