Fix handling of renamed backup files in the core writer (#136898)

* Fix handling of renamed backup files in the core writer

* Adjust mocking

* Raise BackupAgentError instead of KeyError in get_backup_path

* Add specific error indicating backup not found

* Fix tests

* Ensure backups are loaded

* Fix tests

tests/components/backup/test_http.py

@@ -1,7 +1,7 @@
 """Tests for the Backup integration."""
 
 import asyncio
-from collections.abc import AsyncIterator, Iterable
+from collections.abc import AsyncIterator
 from io import BytesIO, StringIO
 import json
 import tarfile
@@ -15,7 +15,12 @@ from homeassistant.components.backup import AddonInfo, AgentBackup, Folder
 from homeassistant.components.backup.const import DATA_MANAGER, DOMAIN
 from homeassistant.core import HomeAssistant
 
-from .common import TEST_BACKUP_ABC123, BackupAgentTest, setup_backup_integration
+from .common import (
+    TEST_BACKUP_ABC123,
+    BackupAgentTest,
+    aiter_from_iter,
+    setup_backup_integration,
+)
 
 from tests.common import MockUser, get_fixture_path
 from tests.typing import ClientSessionGenerator
@@ -35,6 +40,9 @@ async def test_downloading_local_backup(
             "homeassistant.components.backup.backup.CoreLocalBackupAgent.async_get_backup",
             return_value=TEST_BACKUP_ABC123,
         ),
+        patch(
+            "homeassistant.components.backup.backup.CoreLocalBackupAgent.get_backup_path",
+        ),
         patch("pathlib.Path.exists", return_value=True),
         patch(
             "homeassistant.components.backup.http.FileResponse",
@@ -73,9 +81,14 @@ async def test_downloading_local_encrypted_backup_file_not_found(
     await setup_backup_integration(hass)
     client = await hass_client()
 
-    with patch(
-        "homeassistant.components.backup.backup.CoreLocalBackupAgent.async_get_backup",
-        return_value=TEST_BACKUP_ABC123,
+    with (
+        patch(
+            "homeassistant.components.backup.backup.CoreLocalBackupAgent.async_get_backup",
+            return_value=TEST_BACKUP_ABC123,
+        ),
+        patch(
+            "homeassistant.components.backup.backup.CoreLocalBackupAgent.get_backup_path",
+        ),
     ):
         resp = await client.get(
             "/api/backup/download/abc123?agent_id=backup.local&password=blah"
@@ -93,12 +106,6 @@ async def test_downloading_local_encrypted_backup(
     await _test_downloading_encrypted_backup(hass_client, "backup.local")
 
 
-async def aiter_from_iter(iterable: Iterable) -> AsyncIterator:
-    """Convert an iterable to an async iterator."""
-    for i in iterable:
-        yield i
-
-
 @patch.object(BackupAgentTest, "async_download_backup")
 async def test_downloading_remote_encrypted_backup(
     download_mock,