Agent SDK does not reliably honor Claude settings files in `query()`

## Summary

This issue is specifically about `query()`.

I am seeing a mismatch between:

- plain Claude Code behavior when relying on settings files
- SDK `query()` behavior with the same settings context

The main problem is that `query()` injects startup defaults that can override settings-file intent, instead of deferring to Claude Code behavior when no explicit override is provided.

## Versions checked

- `@anthropic-ai/claude-agent-sdk@0.2.63` (bundled Claude Code `2.1.63`)
- `@anthropic-ai/claude-agent-sdk@0.2.72` (bundled Claude Code `2.1.72`)

I observed the same `query()` pattern in both versions.

## What I found in `query()`

In both versions, `query()` assigns a default permission mode in its options destructuring and forwards it to the transport:

- `permissionMode = "default"`
- then passed to process startup as `--permission-mode default`

This means that even when I do not explicitly set `permissionMode`, `query()` still forces one.

I also observed `query()` forwarding `settingSources` explicitly when provided.

## Why this causes SDK vs Claude Code mismatch

In Claude Code CLI usage, if I do not pass `--permission-mode`, behavior can be driven by settings resolution.

In SDK `query()`, permission mode is still injected as `default` unless explicitly changed in SDK options.

So with the same settings files, behavior can diverge because SDK startup arguments are not equivalent to plain Claude Code startup semantics.

## Minimal repro

1. Configure Claude settings so effective permission mode is not `default` (for example `plan`), and confirm expected behavior in plain Claude Code CLI.
2. Run SDK `query()` against the same working directory and settings sources, without passing `permissionMode` in SDK options.
3. Inspect startup/debug logs.

Observed:

- SDK startup includes `--permission-mode default`.
- Effective behavior follows that injected mode rather than fully deferring to settings-file intent.

Expected:

- If `permissionMode` is omitted in SDK options, `query()` should not force `default`.
- `query()` should allow Claude Code settings resolution to determine effective mode, matching CLI semantics.

## Actual vs expected

Actual:

- `query()` injects a default permission mode at startup.
- This can produce behavior different from plain Claude Code with the same settings files.

Expected:

- No implicit permission-mode override when SDK caller did not request one.
- `query()` behavior should match Claude Code settings-driven startup semantics.

## Request

Please update `query()` so omitted options do not silently become effective CLI overrides.

Specifically:

- if `permissionMode` is not provided by caller, do not pass `--permission-mode`
- preserve settings-file-driven behavior unless caller explicitly overrides it
- document this clearly in `query()` option semantics

## Related (context only)

I reviewed related issues around settings behavior, but this report is specifically scoped to `query()` default injection causing SDK vs CLI behavior mismatch.