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/dbgen/dbgen.go

@@ -145,7 +145,6 @@ func ChatMessage(t testing.TB, db database.Store, seed database.ChatMessage) dat
 		Compressed:          []bool{seed.Compressed},
 		TotalCostMicros:     []int64{seed.TotalCostMicros.Int64},
 		RuntimeMs:           []int64{seed.RuntimeMs.Int64},
-		ProviderResponseID:  []string{seed.ProviderResponseID.String},
 	})
 	require.NoError(t, err, "insert chat message")
 	require.Len(t, msgs, 1)

coderd/database/dbgen/dbgen_test.go

@@ -398,7 +398,6 @@ func TestGenerator(t *testing.T) {
 			ContextLimit:        sql.NullInt64{Int64: 77, Valid: true},
 			Compressed:          true,
 			TotalCostMicros:     sql.NullInt64{Int64: 88, Valid: true},
-			ProviderResponseID:  sql.NullString{String: "resp-123", Valid: true},
 		})
 		require.Equal(t, database.ChatMessageRoleAssistant, msg2.Role)
 		require.True(t, msg2.Content.Valid)
@@ -412,7 +411,6 @@ func TestGenerator(t *testing.T) {
 		require.Equal(t, sql.NullInt64{Int64: 77, Valid: true}, msg2.ContextLimit)
 		require.True(t, msg2.Compressed)
 		require.Equal(t, sql.NullInt64{Int64: 88, Valid: true}, msg2.TotalCostMicros)
-		require.Equal(t, sql.NullString{String: "resp-123", Valid: true}, msg2.ProviderResponseID)
 	})
 
 	t.Run("MCPServerConfig", func(t *testing.T) {