ToolSearch from deferred tool loading is not blocked by disallowed_tools, and costs ~10x on single-tool sessions

### Summary

When a session exposes exactly one in-process MCP tool and lists the built-in tools in `disallowed_tools`, the CLI still loads a built-in `ToolSearch` meta-tool through deferred tool loading. The model then calls `ToolSearch` to discover the single MCP tool that was already named in `allowed_tools`. This costs an extra API round trip and about **10x** the total cost of the identical task run with `tools=[]`.

`ToolSearch` is not in the public built-in tool list, so a user writing a denylist has no way to know they should name it.

### Environment

- `claude-agent-sdk` 0.2.128 (latest on PyPI at time of writing)
- bundled Claude Code CLI 2.1.220
- Python 3.12.3, Linux x86_64
- model: `claude-sonnet-5`

### Reproduction

```python
import anyio
from claude_agent_sdk import (ClaudeAgentOptions, ResultMessage, create_sdk_mcp_server,
query, tool)

BUILTINS = ["Bash", "Read", "Write", "Edit", "Glob", "Grep", "WebFetch", "WebSearch",
"NotebookEdit", "Task", "TodoWrite", "BashOutput", "KillShell", "SlashCommand"]

@tool("get_secret_number", "Returns a secret number for demonstration.", {"seed": str})
async def get_secret_number(args: dict) -> dict:
return {"content": [{"type": "text", "text": f"secret={len(args['seed'])}"}]}

server = create_sdk_mcp_server(name="demo", version="1.0.0", tools=[get_secret_number])
FULL = "mcp__demo__get_secret_number"

async def run(zero_base: bool) -> None:
kwargs = dict(
model="claude-sonnet-5",
system_prompt="Answer in one sentence. Use the demo tool when asked.",
mcp_servers={"demo": server},
allowed_tools=[FULL],
disallowed_tools=BUILTINS,
setting_sources=[],
permission_mode="bypassPermissions",
max_turns=5,
)
if zero_base:
kwargs["tools"] = [] # the only difference between the variants
async for msg in query(prompt="Call the demo tool with seed 'demo', then summarise.",
options=ClaudeAgentOptions(**kwargs)):
for block in getattr(msg, "content", []) or []:
if getattr(block, "type", None) == "tool_use":
print("tool_use:", block.name)
if isinstance(msg, ResultMessage):
print("turns:", msg.num_turns, "cost_usd:", msg.total_cost_usd, msg.usage)

anyio.run(run, False) # variant A - denylist only
anyio.run(run, True) # variant B - zero-base allowlist
```

### Observed

**Variant A** (`disallowed_tools` only):

```
tool_use: ToolSearch <- not requested, not in the public tool list
tool_use: mcp__demo__get_secret_number
turns: 3 cost_usd: 0.0683255 cache_creation_input_tokens: 14774
elapsed: 7.79 s
```

**Variant B** (identical, plus `tools=[]`):

```
tool_use: mcp__demo__get_secret_number
turns: 2 cost_usd: 0.00712225
usage: input_tokens=4, cache_creation_input_tokens=1235,
cache_read_input_tokens=1140, output_tokens=100
elapsed: 4.82 s
```

Same task, same model, same tool: **0.0683 USD vs 0.0071 USD**, a factor of 9.6, almost entirely cache-write tokens spent on loading a tool-discovery mechanism for a session that had one tool.

### Expected

Any one of these would resolve it:

1. `ToolSearch` is suppressible by name through `disallowed_tools`, like other built-ins.
2. Deferred tool loading does not engage when the session's total tool count is trivially small — discovering one tool cannot pay for itself.
3. The documentation states plainly that `disallowed_tools` is a denylist and is not sufficient for isolation, and that `tools=[]` is the way to restrict what is available.

### Why this matters beyond cost

Guides and examples commonly show `disallowed_tools` as the way to constrain a session. It is a denylist, so any built-in not named — including one absent from the published tool list — stays reachable. The type stub does say the right thing (`types.py:1770-1771`: *"To restrict which tools are available at all, use `tools`"*), but that line lives in the stub, and the option named `allowed_tools` reads as though it were the restriction. For anyone building a constrained agent, the difference between "these run without prompting" and "these are the only ones that exist" is the whole design.

The related default is worth a docs line too: `setting_sources=None` loads every filesystem source, including the operator's `~/.claude`. For a headless service that must be deterministic, `setting_sources=[]` has to be set explicitly. (#794 and #802 fixed the case where the empty list was ignored; this is about the default itself.)

Read types.py:1770-1771, then run the reported two query variants and compare ToolSearch use, turns, and cost. Trace where deferred tool loading and disallowed_tools are handled; done means an agreed resolution prevents the unintended discovery path or clearly documents that tools=[] is required for restriction, with the reproduction covering the result.

索引モデルが issue の本文から書いたものです。