refactor: drop the vestigial bot_bottle_root/host_db_path re-exports (#352)

paths is the single home now, so stop re-exporting the path helpers from
supervise: remove host_db_path from supervise's imports + __all__ (it was
re-export-only) and drop bot_bottle_root from __all__ (kept as an import,
still used by audit_dir). supervise_types was already clean. Repoint the
last readers (test_supervise imports host_db_path from paths;
test_supervise_edge calls paths.bot_bottle_root) and refresh the doc
mentions. No supervise.bot_bottle_root / supervise.host_db_path references
remain.

Behavior-preserving: full unit suite unchanged (only the pre-existing
/bin/sleep sidecar-init errors).

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

tests/unit/__init__.py

@@ -2,7 +2,7 @@
 
 Isolates ``HOME`` to a throwaway directory for the entire unit suite so
 no test ever reads or writes the real ``~/.bot-bottle`` (state, queue,
-and audit dirs all derive from ``supervise.bot_bottle_root()`` →
+and audit dirs all derive from ``paths.bot_bottle_root()`` →
 ``Path.home()``). Without this, a test that takes a ``flock`` on the
 real audit log can **block indefinitely** when a live bottle's supervise
 sidecar holds that lock — observed as a hung ``coverage run`` at 0% CPU —
@@ -49,8 +49,8 @@ def use_bottle_root(root: Path) -> Callable[[], None]:
     ``BOT_BOTTLE_ROOT`` — the supported override. Returns a callable that
     undoes it (store it as the test's restore hook, or pass to addCleanup).
 
-    Replaces monkey-patching ``supervise.bot_bottle_root``; one env var
-    covers every module and the flat/package copies alike (they all read it)."""
+    Replaces monkey-patching ``paths.bot_bottle_root``; one env var covers
+    every module and the flat/package copies alike (they all read it)."""
     patcher = mock.patch.dict(os.environ, {"BOT_BOTTLE_ROOT": str(root)})
     patcher.start()
     return patcher.stop