Add game_complete event logging to connections #5
Description
Add a game_complete (or puzzle_complete) controllog event at the end of each connections puzzle for leaderboards and analytics.
Context
ChainLex now emits a game_complete event with payload:
- game_id
- model info
- outcome (win/loss)
- scores
- correct guesses
- wall_ms (duration)
- cost tracking
Task
Adapt this pattern for connections with relevant fields:
- puzzle_id
- model
- outcome (solved/failed)
- categories_found (0-4)
- strikes (0-4)
- guesses made
- difficulty breakdown (which categories solved)
- duration
- costs
This enables building leaderboards, puzzle difficulty analysis, and efficiency metrics from controllog.