feat: add client session tracking

[dannykopping]

Refactor client detection and add session tracking

This change extracts client detection logic into a dedicated module and introduces session tracking capabilities for AI bridge interceptions.

Closes #166
Required for coder/internal#1336

Changes

• Extract client detection: Move guessClient function and client constants from bridge.go to new client.go file
• Add Client type: Introduce Client type alias for better type safety and rename ClientClaude to ClientClaudeCode
• Implement session tracking: Add guessSessionID function in session.go to extract session identifiers from requests
• Update interception records: Add ClientSessionID field to InterceptionRecord and call session detection before creating interceptors
• Add comprehensive tests: Include test coverage for both client detection and session ID extraction

The session detection supports:

• Claude Code: Extracts session UUID from metadata.user_id field in JSON body
• Codex: Reads session ID from session_id header
• Mux: Uses X-Mux-Workspace-Id header as session identifier

[dannykopping]

• feat: add client session tracking #198 👈 (View in Graphite)
• feat: record and correlate tool call IDs across interceptions #188
• main

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