Game Mode: unique session names + lever-simulation feedback

[marota]

Summary

Two Game Mode fixes reported from a live session:

1. Duplicate session names are blocked. After finishing "session 3", the
   config screen kept re-suggesting session 3 (a name that already existed),
   and nothing stopped you from starting a run under a name already in the
   shared base.
2. Lever hints now give simulation feedback and can't be double-simulated,
   and injection levers simulate with the default incremental delta instead
   of degrading to "set the amount in the SLD".

Changes

Session naming

• GET /api/game/player-sessions now returns the concrete session_names
  (sorted) alongside session_count.
• The config screen auto-suggests the first free <player> — session <n>
  index by scanning those names — fixing the root cause: the old
  count + 1 heuristic re-suggested a taken name whenever the recorded indices
  had gaps (e.g. {1, 3} → suggested the colliding 3).
• A name that already exists disables ▶ Start with an inline warning (the
  shared base keys retentions by session name, so a duplicate would merge two
  runs).

Lever-simulation feedback (beginner-assistance hints)

• Double-clicking a most-used lever shows a per-row ⏳ simulating… → ✓
  simulated transition (gameBridge.requestLeverInteraction is now
  awaitable).
• A second double-click on a simulated lever is ignored (no accidental
  re-simulation).
• "Simulated" is read from a new simulatedActionIds set on the game-bridge
  snapshot, so a lever also flips to ✓ when its action arrives through the
  recommender's suggestions; a failed run self-clears (its id never enters the
  set) so the lever stays runnable.

Injection levers

• redispatch: / ls: / rc: levers map to the backend dynamic-action id and
  simulate with no target_mw, so _create_dynamic_actions_if_needed applies
  the default incremental injection delta — a double-click runs them
  straight away. Only PST / raw gen_p: / load_p: levers still degrade to
  inspect (a tap / signed setpoint is required).

Tests & docs

• Backend: player_session_count names + endpoint response
  (test_game_solutions.py); regenerated openapi.snapshot.json.
• Frontend: config first-free-index + duplicate-block tests; hints-panel
  simulating→simulated feedback, re-run block, cross-marking, and injection
  default-delta simulate; updated buildLeverInteraction / useLeverInteraction
  tests.
• Updated docs/features/game-mode-codabench.md, the three CLAUDE.md guides,
  the test-conventions guide, and CHANGELOG.md.

Verification

• Frontend: full Vitest suite 1902 passed (3 pre-existing skips); tsc -b
  clean; ESLint 0 errors; code-quality gate OK; standalone parity 30/30 + full
  Layer-1 parity.
• Backend: game + OpenAPI-contract tests green; ruff clean.

🤖 Generated with Claude Code