fix(samples): make a2a human-in-the-loop sample resume after confirmation

[vaibhav-patel]

Summary

Following the README for contributing/samples/a2a/a2a_human_in_loop, the task never completes after the manager approves a reimbursement — it only finishes if the user explicitly asks to "retry". Fixes #5871.

Root cause

The approval runs as a LongRunningFunctionTool (ask_for_approval) on the remote approval_agent, which is a sub-agent of the local root agent. When the user approves, the approval FunctionResponse must be routed back to the remote agent so it can resume the paused tool. Runner._find_agent_to_run only re-routes a function-response turn to the originating agent when the app is resumable, and ResumabilityConfig.is_resumable defaults to False. Under adk web the bare agent is wrapped in an App with no resumability config, so the approval was delivered to the root agent — which has no pending call — and nothing happened. "retry" only worked because it made the model transfer to the remote agent again, starting a brand-new task.

This is a sample-wiring issue; the framework resume path already works (see tests/unittests/a2a/integration/test_client_server.py).

Fix

• Expose the sample as an App with ResumabilityConfig(is_resumable=True) (the same pattern as contributing/samples/hitl/human_tool_confirmation), so the approval is routed back to the remote approval_agent and the long-running tool resumes.
• Fix stale paths in the README run commands (the sample lives under contributing/samples/a2a/) and document how to approve a pending request from the ADK Web UI (send a FunctionResponse via "Send another response", not a plain chat message).

Verification

Verified the routing mechanism deterministically with fake models (no live model needed):

• Fix applied: the sample's app.resumability_config.is_resumable is True, app.root_agent intact.

• Runner._find_agent_to_run routing — the exact decision the fix changes — driven with the session state the Web UI produces after approval (last event = the user's approval FunctionResponse for the long-running call previously emitted by approval_agent):

  App config	approval routed to	result
  is_resumable=True (this fix)	approval_agent	remote agent resumes its paused tool ✓
  is_resumable=False	reimbursement_agent (root)	root re-plans — the A2A human in the loop official sample not working #5871 bug
  bare agent, no App (upstream)	reimbursement_agent (root)	the A2A human in the loop official sample not working #5871 bug

  Confirmed identical in both a non-transferable LlmAgent sub-agent and a BaseAgent sub-agent (the sample's real shape — RemoteA2aAgent is a BaseAgent). 8/8 assertions passed.

• Existing suites pass on the branch: a2a/integration/test_client_server.py (12), test_runners.py (69 — including test_find_agent_to_run_uses_function_response_when_resumable and ..._skips_function_response_when_not_resumable), plus the long-running-tool / resumability / apps suites — 122 passed, 1 skipped, 3 xfailed (the skip/xfail are pre-existing V2-resume markers, unrelated to this change).

Note: no Gemini key was available, so the full two-server live run wasn't exercised; the routing decision the fix relies on is verified at the Runner level and corroborated by the existing unit tests.

Fixes #5871.