refactor: move bot_bottle_root/host_db_path to paths; kill the monkeypatch (#352)

Create bot_bottle/paths.py as the canonical home for the app-root path
helpers (bot_bottle_root, host_db_path, HOST_DB_FILENAME) — foundational,
not supervise- or db-specific. `bot_bottle_root()` now honours a
BOT_BOTTLE_ROOT env override.

Repoint every consumer (supervise, supervise_types, db_store, queue_store,
audit_store, store_manager, bottle_state, cli/supervise, docker/cleanup,
orchestrator/registry) at paths; remove the definitions (and supervise's
duplicate host_db_path) and the now-dead `import sys`. Add paths.py to the
sidecar bundle (Dockerfile.sidecars) for the flat-import copies.

Tests: replace ~12 files' monkeypatching of supervise.bot_bottle_root (and
the flat/pkg/supervise_types triple-patch dance) with a single
`use_bottle_root()` helper that sets BOT_BOTTLE_ROOT — every module and
flat/package copy reads the same env var, so one override covers them all.
Net -97 lines. Behaviour-preserving: full unit suite unchanged (only the
pre-existing /bin/sleep sidecar-init errors remain).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WBMWTEtQdJ4W5UrWuLHCck

tests/unit/test_docker_cleanup.py

@@ -15,7 +15,7 @@ import tempfile
 import unittest
 from pathlib import Path
 
-from bot_bottle import supervise
+from tests.unit import use_bottle_root
 from bot_bottle import bottle_state
 from bot_bottle.backend.docker.cleanup import _list_orphan_state_dirs
 
@@ -23,13 +23,7 @@ from bot_bottle.backend.docker.cleanup import _list_orphan_state_dirs
 class _FakeHomeMixin:
     def _setup_fake_home(self) -> None:
         self._tmp = tempfile.TemporaryDirectory(prefix="docker-cleanup-test.")
-        original = supervise.bot_bottle_root
-
-        def fake_root() -> Path:
-            return Path(self._tmp.name) / ".bot-bottle"
-
-        supervise.bot_bottle_root = fake_root  # type: ignore[assignment]
-        self._restore = lambda: setattr(supervise, "bot_bottle_root", original)
+        self._restore = use_bottle_root(Path(self._tmp.name) / ".bot-bottle")
 
     def _teardown_fake_home(self) -> None:
         self._restore()