feat: remove chat chain mode (#26980)

Removes OpenAI Responses "chain mode" from chatd. Closes CODAGT-445.

- Deletes `chatopenai/responses.go` (chain detection, activation, prompt filtering, response ID extraction) and its tests.
- Deletes the `ChainBroken` classification in `chaterror` and the chatloop retry bookkeeping that disabled chain mode mid-generation.
- Drops the `chain_broken` label from the `coderd_chatd_stream_retries_total` metric.
- Stops reading and writing `chat_messages.provider_response_id`
- Deletes the dead `ClearChatMessageProviderResponseIDsByChatID` query. Dropping the column is a follow-up migration.
- Deletes three chatloop hooks no caller sets (`ReloadMessages`, `DisableChainMode`, `PrepareMessages`), the dead `const AgentChatContextSentinelPath`, and stale chain-mode comments.

🤖 Generated by Coder Agents on behalf of @johnstcn.

coderd/database/queries/chats.sql

@@ -836,8 +836,7 @@ INSERT INTO chat_messages (
     context_limit,
     compressed,
     total_cost_micros,
-    runtime_ms,
-    provider_response_id
+    runtime_ms
 )
 SELECT
     @chat_id::uuid,
@@ -857,8 +856,7 @@ SELECT
     NULLIF(UNNEST(@context_limit::bigint[]), 0),
     UNNEST(@compressed::boolean[]),
     NULLIF(UNNEST(@total_cost_micros::bigint[]), 0),
-    NULLIF(UNNEST(@runtime_ms::bigint[]), 0),
-    NULLIF(UNNEST(@provider_response_id::text[]), '')
+    NULLIF(UNNEST(@runtime_ms::bigint[]), 0)
 RETURNING
     *;
 
@@ -2598,13 +2596,6 @@ WHERE agent_id = @agent_id::uuid
     AND status IN ('waiting', 'running', 'paused', 'pending', 'requires_action')
 ORDER BY updated_at DESC;
 
--- name: ClearChatMessageProviderResponseIDsByChatID :exec
-UPDATE chat_messages
-SET provider_response_id = NULL
-WHERE chat_id = @chat_id::uuid
-    AND deleted = false
-    AND provider_response_id IS NOT NULL;
-
 -- name: SoftDeleteContextFileMessages :exec
 UPDATE chat_messages SET deleted = true
 WHERE chat_id = @chat_id::uuid