The problem is that even when I mount the SSH key into the root home directory (e.g.,

/root/.ssh/id_rsa

with the correct permissions set to 400) I still encounter the same error.

The agent automatically mount's the .ssh folder from the host into the container, making sure all the permissions are set,

how can I run

pip install -e .

in general the agent will add the "working" dir into the PYTHONPATH so that you should not have to manually do "-e ."
That said if you must have it , just add -e . to your "installed packages" section, should work 🤞