examples: simplify agent_improvement_cycle and self_evolving_agent_demo now that rubrics, golden matching, and evolution hooks are in core (#431/#432/#395)

[evekhm]

Now that the canonical evaluation rubrics (#431), golden Q&A matching (#432), and the skill-evolution host hooks (#395) live in core, two older examples still carry hand-rolled copies of that functionality. examples/skill_evolution_lab/ already imports the engine and scores via quality_report.py — no changes needed there.

examples/agent_improvement_cycle (~130 removable lines)

• agent_improvement/prompts.py JUDGE_PROMPT and the {tool_check}/{tool_fail_rule} slots in eval_runner.py are lossy paraphrases of the canonical response_usefulness and tool_usage rubrics in src/bigquery_agent_analytics/evaluation_rubrics.py. Replace the bespoke judge_case() judge call with build_metrics() + Client.evaluate_categorical.
• improver_agent.py build_report_from_eval_results() exists only to fake canonical categories back out of a binary pass flag — delete once the judge emits canonical categories.
• improver_agent.py hand-partitions sessions and hand-formats trajectories; replace with skill_evolution.partition_trajectories() / format_trajectory() (the latter now renders tool calls and correction evidence).

Open decision: the canonical response_usefulness has three categories; the LoopAgent exit condition keys off a binary pass. A partial → pass/fail mapping policy must be chosen (mapping partial to fail makes some currently-passing cycles iterate longer). Also: canonical judging expects traces in BigQuery, but run_eval.py --golden is explicitly a no-BQ path — either keep a local-conversation judging path or accept a BQ dependency on that flag.

examples/self_evolving_agent_demo (~100 lines net)

• analyze_and_evolve.py is a second, weaker evolution engine: _generate_candidate_prompt() (one-shot rewriter), the hand-rolled promotion gate, and _write_prompt_diff() are all superseded by evolve_skill() / select_candidate(..., incumbent_score=) / evolve_skill(artifacts_dir=...).
• analytics/session_metrics.py load_quality_summary() aggregates a deterministic quality_passed stand-in for response_usefulness+tool_usage, superseded by the canonical rubric. (run_sdk_evaluators() is already correct SDK usage; keep.)

Open decision: this demo's narrative is operational-waste-driven evolution (token waste, tool-call overuse), not quality-failure analysis. Routing it through evolve_skill() risks flattening that distinct story — confirm intent before refactoring. The report-shape adapter it needs (quality_passed → sessions[].metrics.response_usefulness.category) is the same bridge agent_improvement_cycle has; write it once, share it.

examples/README.md

Three demos now tell overlapping "agent improves its own prompt" stories with no stated differentiator. Add one line each naming what is distinct: LoopAgent tool-driven loop / operational-waste signal / golden-graded skill evolution.