fix(agent): move archived summary into system prompt for KV cache stability

[chengyongru]

Problem

Archived conversation summaries were injected into the runtime context (user message block) via _build_runtime_context. This has two drawbacks:

1. KV cache waste — the summary changes between turns, so the system prompt prefix cannot reuse cached KV from the previous turn.
2. Consecutive same-role messages — prepending a summary string before the user content can create adjacent user-role messages in edge cases.

Additionally, _last_summary was pop()'ed from session metadata on consumption, meaning it could not survive a process restart.

Approach

1. Move summary into system prompt — build_system_prompt() accepts an optional session_summary and appends it as [Archived Context Summary]. build_messages() forwards session_summary to build_system_prompt() so both the normal path and the ask_user path receive the summary in the system prompt. Since the system prompt is stable across turns (only changes when a new archive is produced), this improves KV cache reuse.

2. Freeze summary format at archive time — _format_summary now uses a static last_active timestamp instead of computing a dynamic "Inactive for X minutes" on every turn, preserving KV cache stability.

3. _last_summary persists in metadata — read with get() instead of pop(), ensuring it survives process restarts. The summary is re-injected every turn via the stable system prompt.

4. estimate_session_prompt_tokens reads summary from metadata — so the token budget estimation accounts for the archived summary accurately.

5. Remove session_summary parameter from _build_runtime_context, maybe_consolidate_by_tokens, and estimate_session_prompt_tokens — these no longer need to handle the summary directly; it flows through build_messages → build_system_prompt instead.

6. /new clears _last_summary — Session.clear() now pops _last_summary from metadata so a fresh session starts clean.

Files changed

• nanobot/agent/autocompact.py — freeze _format_summary output; stop popping _last_summary
• nanobot/agent/context.py — add session_summary to build_messages(); move summary from runtime context to build_system_prompt()
• nanobot/agent/loop.py — pass session_summary to build_messages in all call sites
• nanobot/agent/memory.py — estimate_session_prompt_tokens reads summary from metadata
• nanobot/session/manager.py — clear() removes _last_summary
• tests/agent/test_auto_compact.py — updated assertions + new lifecycle tests
• tests/agent/test_loop_consolidation_tokens.py — updated assertions
• tests/agent/test_unified_session.py — updated assertions

[chengyongru]

Manual tested with langfuse

[Re-bin]

Thanks @chengyongru!