Add a callback for data flow handler removal (#77394)

* Add a callback for when data flows are removed

* Call `async_remove` at the very end

* Handle and log exceptions caught during flow removal

* Log the error as an exception, with a traceback

* Adjust test's expected logging output to match updated format specifier

tests/test_data_entry_flow.py

@@ -1,6 +1,7 @@
 """Test the flow classes."""
 import asyncio
-from unittest.mock import patch
+import logging
+from unittest.mock import Mock, patch
 
 import pytest
 import voluptuous as vol
@@ -149,6 +150,45 @@ async def test_abort_removes_instance(manager):
     assert len(manager.mock_created_entries) == 0
 
 
+async def test_abort_calls_async_remove(manager):
+    """Test abort calling the async_remove FlowHandler method."""
+
+    @manager.mock_reg_handler("test")
+    class TestFlow(data_entry_flow.FlowHandler):
+        async def async_step_init(self, user_input=None):
+            return self.async_abort(reason="reason")
+
+        async_remove = Mock()
+
+    await manager.async_init("test")
+
+    TestFlow.async_remove.assert_called_once()
+
+    assert len(manager.async_progress()) == 0
+    assert len(manager.mock_created_entries) == 0
+
+
+async def test_abort_calls_async_remove_with_exception(manager, caplog):
+    """Test abort calling the async_remove FlowHandler method, with an exception."""
+
+    @manager.mock_reg_handler("test")
+    class TestFlow(data_entry_flow.FlowHandler):
+        async def async_step_init(self, user_input=None):
+            return self.async_abort(reason="reason")
+
+        async_remove = Mock(side_effect=[RuntimeError("error")])
+
+    with caplog.at_level(logging.ERROR):
+        await manager.async_init("test")
+
+    assert "Error removing test config flow: error" in caplog.text
+
+    TestFlow.async_remove.assert_called_once()
+
+    assert len(manager.async_progress()) == 0
+    assert len(manager.mock_created_entries) == 0
+
+
 async def test_create_saves_data(manager):
     """Test creating a config entry."""