refactor(gateway): collapse chat.go four-way duplication

singleChat / singleChatAuto / streamChat / streamChatAuto shared ~260 near-
identical lines (diff after stripping comments was empty). Extract three
shared bodies and shrink all four entry points to thin dispatchers:

- failChat: error → record + writeError, shared ChainErr extraction
  (errors.As returns false for direct-path errors, so the two paths stay
  equivalent without a branch)
- recordChatUsage: exact upstream numbers win, byte estimates fill gaps
- writeChatCompletion: unified ChatCompletion rendering (model name is the
  only direct/auto difference, passed in)
- pumpStream: the full SSE pump (preamble, delta loop, terminal finish +
  usage chunk, [DONE]) — shared by both streaming entries

Behavior change (pinned by TestDirectStreamFailoverAuditSource): direct
streams now pin rec.Source to the source that actually served the stream
after a failover, instead of discarding it (_, usedModel). The audit row
previously recorded the first candidate, which was wrong on failover.

chat.go: 982 → 896 lines (−86).

internal/gateway/gateway_test.go

@@ -702,3 +702,40 @@ type flushRecorder struct {
 }
 
 func (f *flushRecorder) Flush() { f.flushed = true }
+
+// TestDirectStreamFailoverAuditSource: a direct streaming request whose first
+// candidate hard-fails must be served by the fallback, and the audit record's
+// Source must name the source that actually served the stream (not just the
+// first candidate).
+func TestDirectStreamFailoverAuditSource(t *testing.T) {
+	aUp := httptest.NewServer(http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		w.WriteHeader(500)
+		fmt.Fprint(w, `{"error":"boom"}`)
+	}))
+	defer aUp.Close()
+	bUp := mockUpstream()
+	defer bUp.Close()
+	g := newTestGateway(t,
+		// Both sources expose the same model id so the direct scheduler has a
+		// real fallback candidate after a hard-fails; b is the healthy one.
+		config.Source{Name: "a", BaseURL: aUp.URL, Adapter: "openai", Models: []config.Model{{ID: "m"}}},
+		config.Source{Name: "b", BaseURL: bUp.URL, Adapter: "openai", Models: []config.Model{{ID: "m"}}},
+	)
+	body := doReq(t, g, "POST", "/v1/chat/completions",
+		`{"model":"m","stream":true,"messages":[{"role":"user","content":"hi"}]}`)
+	if body.Code != 200 {
+		t.Fatalf("status=%d body=%s", body.Code, body.Body.String())
+	}
+	sb := body.Body.String()
+	if !strings.Contains(sb, `"finish_reason":"stop"`) || !strings.Contains(sb, "[DONE]") {
+		t.Fatalf("stream incomplete: %s", sb)
+	}
+	recs := g.stats.AuditRecords(0, 0, "")
+	if len(recs) == 0 {
+		t.Fatal("no audit records")
+	}
+	last := recs[len(recs)-1]
+	if last.Source != "b" || !last.OK {
+		t.Fatalf("audit rec source=%q ok=%v, want source=b ok=true (actual serving source)", last.Source, last.OK)
+	}
+}