docs: Update agent-mode-design for Agent SDK migration [doc-updater]

[james-in-a-box]

docs: Update agent-mode-design for Agent SDK migration

Update code example in agent-mode-design.md that was rendered stale by
commit 487fea5 ("Migrate orchestrator from claude --print to Agent SDK").

The "Anti-pattern 3" section's "Right approach" example previously showed
["claude", "--print", "--max-turns", "1", ...] as the correct way to
delegate LLM calls from the orchestrator to sandbox containers. With the
migration, the orchestrator now uses build_agent_command() which returns
python3 -m egg_agent — not the claude CLI. The example now correctly
reflects this pattern.

Issue: none

Test plan:

• Verify the updated code example matches shared/egg_agent/command.py
build_agent_command() signature and usage.

Authored-by: egg

[egg-reviewer]

No agent-mode design concerns.

This is a documentation-only change that updates the "Anti-pattern 3" code example to reflect the build_agent_command() migration. The updated example correctly shows the current pattern.

— Authored by egg

[egg-reviewer]

Documentation change accurately reflects the codebase. Verified:

• Import path from egg_agent import build_agent_command matches shared/egg_agent/__init__.py export and existing usage in orchestrator/routes/pipelines.py.
• build_agent_command(prompt=..., max_turns=1) matches the real signature in shared/egg_agent/command.py.
• Return type list[str] is compatible with the command= parameter on spawn_agent_container().

No issues.

— Authored by egg

[james-in-a-box]

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