feat: Add LLM council sample to workflow patterns

[simonraj79]

Link to Issue or Description of Change

2. Or, if no issue exists, describe the change:

Problem:
The contributing/samples catalog demonstrates fan-out/fan-in with plain
function nodes (workflows/fan_out_fan_in) but has no sample showing a
complete multi-LLM deliberation pattern: parallel Agent nodes, two chained
fan-out/fan-in rounds, structured output contracts between LLM stages, and
deterministic post-processing of LLM votes. The "LLM council" pattern
(popularized by Andrej Karpathy's llm-council)
is a natural fit and a frequently requested multi-agent shape.

Solution:
Add contributing/samples/patterns/llm_council — a self-contained,
three-stage council in a single Workflow:

1. First opinions — three persona agents (pragmatist, skeptic,
   visionary) answer in parallel via a fan-out tuple.
2. Anonymized peer review — a function node relabels the JoinNode
   output as "Response A/B/C"; a second fan-out has every member rank all
   responses blind, ending with a machine-parseable
   FINAL RANKING: B > A > C ballot line.
3. Tally + synthesis — tally_ballots (plain Python) parses the ballots
   and computes the average-rank leaderboard deterministically; a chairman
   agent synthesizes the final answer and de-anonymizes the verdict via a
   roster only it can see.

Design points the sample teaches:

• Chained fan-out/fan-in rounds with two JoinNodes in one graph.
• One shared static_instruction across all seven agents, so every LLM call
  in a session carries a byte-identical system instruction (keeps the
  cacheable prefix stable; the adk web System Instruction Performance
  Analysis reports no cache-breaking instruction changes). Persona and stage
  tasks ride in the dynamic instruction, which ADK sends as user content
  when static_instruction is set.
• Selective state exposure via instruction templating: reviewers see the
  anonymized {transcript}; only the chairman sees {roster}, which keeps
  the peer review blind.
• LLM output → code contract: reviewers must emit an exact ballot line;
  arithmetic is done in a function node, never by the model.

Testing Plan

Unit Tests:

• I have added or updated unit tests for my change.
• All unit tests pass locally.

The sample is covered by the existing sample harness in
tests/unittests/test_samples.py (test_sample_loads auto-discovers it).

pytest tests/unittests/test_samples.py -k llm_council
1 passed, 278 deselected in 2.78s

Full local unit suite (Python 3.11, Windows):

19 failed, 9056 passed, 64 skipped, 18 xfailed, 1 xpassed in 559.57s (0:09:19)

All 19 failures are pre-existing Windows line-ending issues in
tests/unittests/tools/environment/ file-tool tests, unrelated to this
change — the branch is main plus a single commit that only adds files
under contributing/samples/ and touches no source code.

scripts/compliance_checks.py and all pre-commit hooks (isort, pyink,
addlicense, mdformat) pass on both files.

Manual End-to-End (E2E) Tests:

Setup: adk web contributing/samples/patterns --port 8000 with a Gemini API
key in the sample folder's .env, select llm_council, using the three
Sample Inputs from the README.

Three full runs verified via the dev UI event stream and trace viewer:

• All 13 nodes execute per invocation; the two fan-out stages run their three
  agents concurrently (stage wall-clock = slowest member, confirmed in
  Traces).
• All 3 reviewer ballots parsed in every run; tally_ballots leaderboard
  matches a hand-computed average of the ballots each time.
• Chairman reply contains the four required sections and reproduces the
  leaderboard table exactly, de-anonymized via the roster.
• Total invocation latency across the three runs: 48.8s → 33.9s → 32.2s
  (improvements during development: shared static_instruction, 500-word
  chairman cap).
• With the shared static_instruction, the dev UI shows no
  System-Instruction cache-miss performance warnings on any event
  (previously flagged on every LLM event).

Screenshots of the executed graph, event stream, and chairman verdict
attached below.

Checklist

• I have read the CONTRIBUTING.md document.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have added tests that prove my fix is effective or that my feature works.
• New and existing unit tests pass locally with my changes.
• I have manually tested my changes end-to-end.
• Any dependent changes have been merged and published in downstream modules.

Additional context

The sample follows the structure documented in the repo's sample-authoring
guidance (agent.py + README with Overview / Sample Inputs / Graph / How To /
Related Guides) and does not set an explicit model=, per sample guidelines.
The README notes how to reproduce Karpathy's original one-model-per-seat
configuration.