feat(manifest)!: record per volume what the run established

A finished generation cannot show whether a volume held a database, nor whether a dump was produced for it: under --only-sql a failed dump falls back to a file copy, and the resulting files/ tree looks like any other copy. The run knows both and threw the knowledge away as a printed warning, leaving every reader to guess from file names.

Each generation now carries a manifest.json stating its layout and, per volume, database / dumped / engine. baudolo.generation is the single place those names are spelled; restore/paths.py, backup/db.py and backup/volume.py stop repeating them. It is deliberately import-free so a consumer can read the manifest with nothing but json, on hosts where this package is not installed.

BREAKING CHANGE: BackupException is renamed BackupError. The rename is atomic across the ten modules that define or import it, three of which also carry the manifest change, so it lands in this commit rather than a separate one that could not import.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

tests/e2e/test_e2e_only_sql_mixed_run.py

@@ -1,5 +1,8 @@
+import json
 import unittest
 
+from baudolo.generation import MANIFEST_FILE
+
 from .helpers import (
     POSTGRES_DATA_DIR,
     POSTGRES_IMAGE,
@@ -179,3 +182,21 @@ class TestE2EOnlySqlMixedRun(unittest.TestCase):
             (base / "files").exists(),
             f"Expected non-DB volume files backup to exist at: {base / 'files'}",
         )
+
+    def manifest(self) -> dict:
+        generation = backup_path(
+            self.backups_dir, self.repo_name, self.version, self.db_volume
+        ).parent
+        return json.loads((generation / MANIFEST_FILE).read_text(encoding="utf-8"))
+
+    def test_the_manifest_records_the_dumped_volume_as_dumped(self) -> None:
+        self.assertEqual(
+            self.manifest()["volumes"][self.db_volume],
+            {"database": True, "dumped": True, "engine": "postgres"},
+        )
+
+    def test_the_manifest_records_the_plain_volume_as_no_database(self) -> None:
+        self.assertEqual(
+            self.manifest()["volumes"][self.files_volume],
+            {"database": False, "dumped": False, "engine": None},
+        )