chat: fix Responses API tool-chaining, context limits, and streaming correctness (#1080)

## Summary

Three rounds of review against the [Azure OpenAI Responses API
docs](https://learn.microsoft.com/en-us/azure/foundry/openai/how-to/responses)
(using Claude Opus 4.6 and GPT-5.5 as parallel review subagents)
identified and fixed several correctness bugs and robustness gaps in the
AI chat implementation.

---

## Critical fixes

### C1 — Parallel streaming tool calls created forked conversation
branches

Previously, `ProcessStreamingUpdatesAsync` fired a separate API
continuation per tool call inline during the stream. With N parallel
tool calls this created N independent conversation branches — each
continuation only saw its own tool result, not the others.

**Fix:** Two-phase pattern — buffer all `FunctionCallResponseItem`s
during the stream, execute them sequentially after the stream completes,
then make **one** continuation with all outputs. Matches the
non-streaming behavior.

### C2 — Context length errors not caught in streaming path

`ClientResultException` from a context-window overflow propagates
through `await foreach` but C# prohibits `yield return` inside a
`try/catch` block (CS1626).

**Fix:** Added `RethrowContextLengthErrors` helper that puts `try/catch`
only around `MoveNextAsync`, with `yield return` outside — the only
CS1626-safe pattern for exception remapping in async iterators.

---

## High fixes

### H1 — SSE error event lost on mid-stream exception

The second `catch (Exception ex)` block in `StreamMessage` was missing
its `try { await Response.WriteAsync(...) } catch {}` body, so clients
received no signal when the stream was interrupted.

### H2 — `CloneOptionsWithPreviousResponseId` copied only 3 of 14 fields

Tool-call continuation legs inherited `Instructions`,
`PreviousResponseId`, and `Tools` — but not `EndUserId`, `Temperature`,
`TopP`, `TruncationMode`, `MaxOutputTokenCount`, `TextOptions`,
`ParallelToolCallsEnabled`, `StoredOutputEnabled`, `ToolChoice`,
`ServiceTier`, or `Metadata`. Continuations were silently using defaults
for all of those.

### H3 — Context length detection relied on substring matching only

**Fix:** `IsContextLengthError` now parses the structured JSON error
body via `TryExtractErrorCode` and checks the `error.code` field first
(`context_length_exceeded`, `token_limit_exceeded`). Also handles HTTP
413. Falls back to message substring matching.

---

## Medium fixes (from second review pass)

- **`ParseToolArguments` unguarded in non-streaming path** — a
`JsonException` on malformed model-generated arguments would bubble up
as a 500. Now caught identically to the streaming path, returning an
error `FunctionCallOutputResponseItem` so the model can recover.
- **`strictModeEnabled: false` for MCP tool registration** — the MCP
.NET SDK generates schemas that don't satisfy OpenAI strict-mode
constraints (optional params not in `required`, no
`additionalProperties: false`, nullable union types). A single
non-conforming schema with `strictModeEnabled: true` causes a 400 that
blocks all tools.
- **`currentLegResponseId` null guard** — if the API never emits
`StreamingResponseCreatedUpdate`, the continuation would fire with
`PreviousResponseId = null`, causing a confusing 400. Now throws
`InvalidOperationException` with a diagnostic message.
- **Log original exception in mid-stream context-limit handler** — was
logging a freshly constructed `InvalidOperationException`, discarding
the original stack trace and `PreviousResponseId`.

---

## Bonus

- **`EndUserId` wired up** — `CreateResponseOptionsAsync` now sets
`options.EndUserId` (the SDK exposes it; the previous code discarded
it). Enables Azure OpenAI abuse monitoring and Defender prompt-shield
correlation.
- **`LogMcpToolArgumentParseError`** logger message added.
- **`ConversationContextLimitExceededException`** domain exception with
`PreviousResponseId` property.

---

## Files changed

| File | Changes |
|------|---------|
| `EssentialCSharp.Chat.Shared/Services/AIChatService.cs` | All
service-level fixes |
|
`EssentialCSharp.Chat.Shared/Services/ConversationContextLimitExceededException.cs`
| New domain exception |
| `EssentialCSharp.Web/Controllers/ChatController.cs` | Context-limit
handling, SSE error write, logging |

Author: BenjaminMichaelis