fix(adk): resolve multi-turn conversation failure with None user_message

[MisterTK]

Summary

• Fix two bugs in adk_agent.py that caused multi-turn conversations to fail with ValueError: Both invocation_id and new_message are None error on the second message

Problem

When using CopilotKit with ag-ui-adk, multi-turn conversations fail on the second message. The first message works correctly, but subsequent messages throw the error from Google ADK.

Root Cause

Two bugs combine to cause this issue:

Bug 1: Incorrect conditional (line 1080)

# Buggy:
user_message = await self._convert_latest_message(input, unseen_messages) if message_batch else None

The condition if message_batch else None incorrectly sets user_message to None when message_batch was not explicitly passed (which is the normal case for direct calls via the run method), even when unseen_messages contained valid user messages.

Bug 2: No fallback when unseen_messages is empty (line ~1187)

When unseen_messages is empty (because all messages were already marked as "processed" by ID), there was no fallback to extract the latest user message from input.messages. This happens when:

1. CopilotKit sends all messages with the same or reused IDs
2. The first request marks message IDs as processed
3. On the second request, _get_unseen_messages() returns empty
4. Code falls through without a valid user message
5. Google ADK throws the error

Solution

1. Remove the incorrect conditional so _convert_latest_message is always called when there are unseen messages
2. Add a fallback to extract from input.messages when user_message is None

Test Plan

• Tested with CopilotKit frontend - multi-turn conversations now work correctly
• First message: 200 OK with RUN_STARTED -> TEXT_MESSAGE -> RUN_FINISHED
• Second message (previously failed): 200 OK with same event sequence
• Third+ messages: Continue to work correctly

Fixes #769

[contextablemark]

Hi @MisterTK - Thank you for your analysis and for proposing a fix. Would it be possible to add a test (under https://github.com/ag-ui-protocol/ag-ui/tree/main/integrations/adk-middleware/python/tests) to simulate this sequence in order to help verify the fix and guard against regressions in the future?