refactor(server): extract context.py into focused modules

Split the monolithic context.py (117 lines) into five purpose-specific
modules following single-responsibility principle:

- config.py: Server-level constants (DATA_DIR, SESSIONS_DIR, PORT,
  STALE_EVENT_AGE, _state_lock)
- agents.py: Agent-specific paths and caches (CLAUDE_PROJECTS_DIR,
  CODEX_SESSIONS_DIR, discovery caches)
- auth.py: Authentication token generation/validation for spawn endpoint
- spawn_config.py: Spawn feature configuration (PENDING_SPAWNS_DIR,
  rate limiting, projects watcher thread)
- zellij.py: Zellij binary resolution and session management constants

This refactoring improves:
- Code navigation: Find relevant constants by domain, not alphabetically
- Testing: Each module can be tested in isolation
- Import clarity: Mixins import only what they need
- Future maintenance: Changes to one domain don't risk breaking others

All mixins updated to import from new module locations. Tests updated
to use new import paths.

Includes PROPOSED_CODE_FILE_REORGANIZATION_PLAN.md documenting the
rationale and mapping from old to new locations.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

amc_server/spawn_config.py

@@ -0,0 +1,40 @@
+"""Spawn feature config: paths, locks, rate limiting, projects watcher."""
+
+import threading
+from pathlib import Path
+
+from amc_server.config import DATA_DIR
+
+# Pending spawn registry
+PENDING_SPAWNS_DIR = DATA_DIR / "pending_spawns"
+
+# Pending spawn TTL: how long to keep unmatched spawn records (seconds)
+PENDING_SPAWN_TTL = 60
+
+# Projects directory for spawning agents
+PROJECTS_DIR = Path.home() / 'projects'
+
+# Lock for serializing spawn operations (prevents Zellij race conditions)
+_spawn_lock = threading.Lock()
+
+# Rate limiting: track last spawn time per project (prevents spam)
+_spawn_timestamps: dict[str, float] = {}
+SPAWN_COOLDOWN_SEC = 10.0
+
+
+def start_projects_watcher():
+    """Start background thread to refresh projects cache every 5 minutes."""
+    import logging
+    from amc_server.mixins.spawn import load_projects_cache
+
+    def _watch_loop():
+        import time
+        while True:
+            try:
+                time.sleep(300)
+                load_projects_cache()
+            except Exception:
+                logging.exception('Projects cache refresh failed')
+
+    thread = threading.Thread(target=_watch_loop, daemon=True)
+    thread.start()