fix(flows): terminate invocation at tool-level EUC

[doughayden]

Link to Issue or Description of Change

1. Link to an existing issue (if applicable):

• Closes: Tool-level auth continues invocation past the EUC event #5637

This change adds invocation_context.end_invocation = True after the auth event yield in _postprocess_handle_function_calls_async, mirroring the existing termination signal in _resolve_toolset_auth. Tool-level auth now terminates symmetrically with toolset-level auth at the EUC, instead of continuing for one more LLM call.

Testing Plan

Unit Tests:

• I have added or updated unit tests for my change.
• All unit tests pass locally.

Three existing tests in test_functions_request_euc.py had assertions tied to the trailing post-EUC LLM call:

• test_function_request_euc: adds assert len(mock_model.requests) == 1 to anchor the new termination behavior.
• test_function_get_auth_response: events[-3] → events[-2] for the auth event lookup, since the auth event is now second-to-last.
• test_function_get_auth_response_partial: same events[-3] → events[-2] change, plus the two len(mock_model.requests) assertions drop by 1 (3 → 2 and 4 → 3).

$ pytest tests/unittests/flows/llm_flows/test_functions_request_euc.py
======================== 3 passed, 17 warnings in 1.31s ========================

$ pytest tests/unittests/
=============== 5695 passed, 2308 warnings in 122.89s (0:02:02) ================

Manual End-to-End (E2E) Tests:

A self-contained Runner-based reproduction is at https://github.com/doughayden/adk-issue-examples/tree/main/04-tool_level_auth_continuation. The agent definition (agent.py) wires up an OpenAPIToolset against a local OAuth2 test server. main.py constructs an InMemoryRunner, applies the workaround for #5327 (get_auth_config = lambda: None) at runtime to land on the tool-level auth path, and sends a tool-triggering prompt. The --apply-fix flag monkey-patches the proposed fix to demonstrate the resolution end-to-end.

Without the fix:

👤 User: What's the weather in San Francisco?
🌤️  Weather Assistant event stream:

    [function_call] get_weather by WeatherAssistant
    [auth_event] adk_request_credential by WeatherAssistant
    [function_response] get_weather by WeatherAssistant
    [post_euc_text] WeatherAssistant: "I'm sorry, I cannot retrieve the weather for San Francisco at the moment. It ..."

Event counts:
    function_calls: 1
    auth_events: 1
    function_responses: 1
    text_events: 1
    post_euc_text_events: 1

✅ Bug reproduced: 1 text event(s) after the EUC (agent loop continued past adk_request_credential).

With the fix:

👤 User: What's the weather in San Francisco?
🌤️  Weather Assistant event stream:

    [function_call] get_weather by WeatherAssistant
    [auth_event] adk_request_credential by WeatherAssistant
    [function_response] get_weather by WeatherAssistant

Event counts:
    function_calls: 1
    auth_events: 1
    function_responses: 1
    text_events: 0
    post_euc_text_events: 0

✅ Fix verified: no LLM events after the EUC.

Checklist

• I have read the CONTRIBUTING.md document.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have added tests that prove my fix is effective or that my feature works.
• New and existing unit tests pass locally with my changes.
• I have manually tested my changes end-to-end.
• Any dependent changes have been merged and published in downstream modules.

Additional context

Alternative considered:

A reorder of the yields (yield auth_event last so last_event.is_final_response() returns True) would also fix the loop termination in a single iteration without needing the flag. I went with end_invocation = True to preserve the observable event order and to match the existing pattern in _resolve_toolset_auth. Happy to switch if maintainers prefer the reorder.

Related:

The same yield site at lines 1126-1130 also produces tool_confirmation_event for HITL with the same long_running_tool_ids shape and the same termination gap. This PR scopes to auth_event only. Happy to open a follow-up PR with the same fix for tool_confirmation_event if the team agrees with the approach here.