## Problem
Flaky test:
`TestCloseDuringShutdownContextCanceledShouldRetryOnNewReplica`
(coder/internal#1371)
The test intermittently fails because the chat ends up in `waiting`
status instead of `pending` after server shutdown.
## Root Cause
There is a race condition in `processChat` where `runChat` completes
successfully just as the server context is being canceled during
`Close()`. The sequence:
1. Server calls `Close()`, canceling the server context.
2. The LLM HTTP response has already been fully written by the mock
server (the stream closes normally before context cancellation
propagates to the HTTP client).
3. `runChat` returns `nil` (success) instead of `context.Canceled`.
4. The existing `isShutdownCancellation` check only runs when `runChat`
returns an error, so the shutdown is not detected.
5. `processChat`'s deferred cleanup marks the chat as `waiting` instead
of `pending`.
6. The test's assertion that the chat is `pending` never becomes true.
This race is timing-dependent — it only triggers when the mock server's
HTTP response completes in the narrow window between context
cancellation being initiated and it propagating through the HTTP
transport layer.
## Fix
Add a server context check after `runChat` returns successfully. If the
server is shutting down (`ctx.Err() != nil`), override the status to
`pending` so another replica can pick up the chat.
This is the same pattern already used for the error path
(`isShutdownCancellation`), extended to cover the success path.