fix(batch): read invocations from tool input and fix concurrency error

[dosvk]

Fix two bugs preventing the batch tool from executing sub-tools:

1. Read invocations from tool['input']['invocations'] instead of kwargs,
   which only contains framework state (agent, model, etc.) and never
   the tool input parameters.

2. Pass record_direct_tool_call=False when calling sub-tools to avoid
   ConcurrencyException from the agent invocation lock that is already
   held by the batch tool execution.

Update tests to pass invocations via tool['input'] to match the real
SDK calling convention.

Closes #413

Description

Fix two bugs in the batch tool that prevented any sub-tool execution.

Bug 1 (line 97): kwargs.get("invocations", []) always returned empty because
module-based tools receive their inputs in the tool dict, not kwargs. Fixed
to tool.get("input", {}).get("invocations", []).

Bug 2 (line 112): tool_fn(**arguments) raised ConcurrencyException because
the agent invocation lock was already held. Fixed by passing
record_direct_tool_call=False to skip the lock and message recording.

Related Issues

Closes #413

Documentation PR

N/A

Type of Change

Bug fix

Testing

• Fixed existing tests to pass invocations via tool["input"] (matching real SDK calling convention)
• Added test for missing input key (graceful fallback)
• Added assertion verifying sub-tools called with record_direct_tool_call=False
• Verified manually with real agent: batch now executes all sub-tools successfully
• 6 tests passing, 0 failures

Evidence

Before fix (batch returns 0 results, agent falls back to individual calls):

=== Testing batch tool ===
Asking agent to get current time in multiple timezones using batch...

I'll use the batch tool to get the current time in both UTC and US/Pacific simultaneously.
Tool #1: batch
It seems there was an issue with the batch execution. Let me try getting both times individually:
Tool #2: current_time

Tool #3: current_time
Here are the current times:

- **UTC**: 2026-04-02T16:22:03.529741+00:00 (4:22:03 PM)
- **US/Pacific**: 2026-04-02T09:22:04.658259-07:00 (9:22:04 AM)

The Pacific time is 7 hours behind UTC, which is expected during Pacific Daylight Time (PDT) when daylight saving time is in effect.
=== Result ===
Here are the current times:

- **UTC**: 2026-04-02T16:22:03.529741+00:00 (4:22:03 PM)
- **US/Pacific**: 2026-04-02T09:22:04.658259-07:00 (9:22:04 AM)

The Pacific time is 7 hours behind UTC, which is expected during Pacific Daylight Time (PDT) when daylight saving time is in effect.

After fix (batch executes all sub-tools in one call):

=== Testing batch tool ===
Asking agent to get current time in multiple timezones using batch...

I'll use the batch tool to get the current time in both UTC and US/Pacific timezones simultaneously.
Tool #1: batch
Here are the current times in both timezones:

**UTC**: 2026-04-02T16:28:14.740848+00:00  
**US/Pacific**: 2026-04-02T09:28:14.742302-07:00

The Pacific time is 7 hours behind UTC, showing the current daylight saving time offset.
=== Result ===
Here are the current times in both timezones:

**UTC**: 2026-04-02T16:28:14.740848+00:00  
**US/Pacific**: 2026-04-02T09:28:14.742302-07:00

The Pacific time is 7 hours behind UTC, showing the current daylight saving time offset.

• I ran hatch run prepare

Checklist

• I have read the CONTRIBUTING document
• I have added any necessary tests that prove my fix is effective or my feature works
• I have updated the documentation accordingly
• I have added an appropriate example to the documentation to outline the feature
• My changes generate no new warnings
• Any dependent changes have been merged and published

---

By submitting this pull request, I confirm that you can use, modify, copy, and redistribute this contribution, under the terms of your choice.