Run Headless Agent Sessions inside the API container

[ExtraToast]

Design: #59 (the glossary and ADRs). Use the glossary's terms.

What to build

The Headless Run Mode keeps working in the new runtime. The user starts a Headless Agent Session with a prompt, the agent works through it as agent inside the container with no terminal, its Transcript is stored, and the session ends Stopped or Failed. "Job" wording is removed in favour of Run Mode.

Implements ADR 0001: Agent Sessions run inside the API container.

Acceptance criteria

• Starting a Headless Agent Session runs the agent non-interactively as agent in its Workspace.
• Completion ends Stopped and an error ends Failed, and the Transcript is stored in both cases.
• Cancelling ends the process and marks the Agent Session Stopped.
• Headless Agent Sessions are never Suspended by Idle Timeout.

Blocked by

• Run Claude and Codex Agent Sessions with Agent Login on the home volume #64