docs(ai_client): rename send_result to send in 3 current docs

Doc consistency: guide_ai_client.md, guide_app_controller.md, and
the error_handling styleguide now reference the new symbol name.

Also fixes two consistency issues in error_handling.md introduced by
the mechanical rename:
1. The 'Deprecation: send -> send_result' section (lines 623-642) was
   rewritten as a 'Historical deprecation (added 2026-06-15, reverted
   2026-06-16)' note that points to the relevant track specs.
2. Line 204 (the 'Current State Audit' summary for src/ai_client.py)
   had a self-contradictory claim ('send() is the new public API;
   send() is @deprecated') after the rename. Updated to describe
   the canonical public API.

Historical archives (conductor/tracks/*/spec.md, conductor/tracks/*/plan.md,
docs/reports/*) are NOT modified - they document the 2026-06-15
public_api_migration decision and stay as historical record.

docs/guide_ai_client.md

@@ -465,7 +465,7 @@ meaning — do not overload `UNKNOWN` when a new failure mode surfaces
 
 ### Public API
 
-- **`ai_client.send_result(...)`** — the public API. Returns
+- **`ai_client.send(...)`** — the public API. Returns
   `Result[str, ErrorInfo]`. Accepts 13+ parameters including 8 callbacks.
   Internally calls `_send_<vendor>()` for the active provider (the
   vendor functions return `Result[str]` directly).
@@ -476,7 +476,7 @@ meaning — do not overload `UNKNOWN` when a new failure mode surfaces
 from src import ai_client
 from src.result_types import ErrorKind
 
-r = ai_client.send_result("system prompt", "user message")
+r = ai_client.send("system prompt", "user message")
 if not r.ok:
     for err in r.errors:
         log.error(err.ui_message())
@@ -487,7 +487,7 @@ print(r.data)
 
 ### Migration Notes for Existing Callers
 
-- All production call sites and tests now use `send_result()`. The
+- All production call sites and tests now use `send()`. The
   legacy `send()` function was removed in the
   `public_api_migration_and_ui_polish_20260615` track.
 - Tests that mock `ai_client._send_<vendor>` should use the
@@ -514,7 +514,7 @@ print(r.data)
 - **[docs/reports/qwen_llama_grok_followup_audit_20260611.md](qwen_llama_grok_followup_audit_20260611.md)** — Audit of the parent track's gaps; follow-up track `qwen_llama_grok_followup_20260611` covers them
 - **Gemini / Gemini CLI thinking-format compatibility (deferred from `ai_loop_regressions_20260614`)** — the user's complaint included Gemini; the likely cause is a format mismatch between the Gemini SDK output and `parse_thinking_trace`. Empirically investigate by running a Gemini request that produces reasoning and inspecting the raw `resp.text`. **Resolved 2026-06-15 by `doeh_test_thinking_cleanup_20260615`**: the `google-genai` SDK filters `thought=True` parts out of `resp.text`. The new helper `_extract_gemini_thoughts` in `src/ai_client.py` scans `resp.candidates[0].content.parts` for `thought=True` and prepends the concatenated text as `<thinking>...</thinking>` so `parse_thinking_trace` extracts it. 5 regression tests in `tests/test_gemini_thinking_format.py` cover the helper and the wrap path. See [track spec](../conductor/tracks/doeh_test_thinking_cleanup_20260615/spec.md) §3.2 G15.
 - **`<think>` (half-width) marker support in thinking_parser (deferred from `ai_loop_regressions_20260614`)** — user screenshot showed `<think>...</think>` format; current `parse_thinking_trace` requires `<thinking>`. The change is small (~3 lines in `src/thinking_parser.py:9`). **Resolved 2026-06-15 by `doeh_test_thinking_cleanup_20260615`**: the `tag_pattern` regex in `src/thinking_parser.py:20` now also matches `<think>...</think>` (the backreference `\1` matches the closing tag). New test `test_parse_half_width_think_tag` in `tests/test_thinking_trace.py`. All 8 thinking_trace tests pass.
-- **Public API Result Migration (planned, separate track `public_api_migration_20260606`)** — the 5 production + 63 test call sites not migrated in this track; the follow-up removes the deprecated `ai_client.send()`. See [parent track spec](../conductor/tracks/data_oriented_error_handling_20260606/spec.md) §12.1. **Completed 2026-06-15 by `public_api_migration_and_ui_polish_20260615`**: 3 remaining production call sites (src/conductor_tech_lead.py:68, src/orchestrator_pm.py:86, src/multi_agent_conductor.py:591) + 18 test files (11 call-site + 7 production-affected mock) were migrated to `send_result()`. The deprecated `send()` function was removed from `src/ai_client.py`. See [track spec](../conductor/tracks/public_api_migration_and_ui_polish_20260615/spec.md).
+- **Public API Result Migration (planned, separate track `public_api_migration_20260606`)** — the 5 production + 63 test call sites not migrated in this track; the follow-up removes the deprecated `ai_client.send()`. See [parent track spec](../conductor/tracks/data_oriented_error_handling_20260606/spec.md) §12.1. **Completed 2026-06-15 by `public_api_migration_and_ui_polish_20260615`**: 3 remaining production call sites (src/conductor_tech_lead.py:68, src/orchestrator_pm.py:86, src/multi_agent_conductor.py:591) + 18 test files (11 call-site + 7 production-affected mock) were migrated to `send()`. The deprecated `send()` function was removed from `src/ai_client.py`. See [track spec](../conductor/tracks/public_api_migration_and_ui_polish_20260615/spec.md).
 - **`doeh_test_thinking_cleanup_20260615` (shipped 2026-06-15)** — cleanup follow-up to `data_oriented_error_handling_20260606` and `ai_loop_regressions_20260614`. Fixed: 1 CRITICAL production regression (`_api_generate` `NameError` from commit `2b7b571a`), 11 test mock bugs, 2 deferred bugs (Gemini thinking format, `<think>` half-width marker), and 2 housekeeping items (state.toml duplicate keys, tracks.md row 24). See [track spec](../conductor/tracks/doeh_test_thinking_cleanup_20260615/spec.md) + [plan](../conductor/tracks/doeh_test_thinking_cleanup_20260615/plan.md).
 
 ---

docs/guide_app_controller.md

@@ -433,7 +433,7 @@ if not target_key:
 Example (line 309):
 ```python
 try:
-    result = ai_client.send_result(...)
+    result = ai_client.send(...)
     return result.data
 except Exception as e:
     raise HTTPException(status_code=500, detail=f"AI call failed: {e}")