Sign the completion and the probe with the same token (V-673)

llm.Client carries a bearer credential and sets it on the completion, and
Pair signs the /health probe with it too. An unsigned probe would answer 401,
Pair would read that as a card that is busy, and every workstation turn would
fall back to the resident model with nothing naming why.

The token comes from workstation.token, expanded from MAVEN_GPU_TOKEN like
every other secret in that file. Missing, and voicewire says so at startup:
the fallback is silent by design and this failure would otherwise be
invisible.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01ESv8hqNPseYt1CnotZpqDz

internal/llm/remote_test.go

@@ -250,3 +250,35 @@ func TestNoFloorIsAnError(t *testing.T) {
 		t.Fatalf("err = %v, want ErrNoFloor", err)
 	}
 }
+
+// The workstation is behind mavgpud, which requires a bearer token on the
+// completion and on /health alike. A probe that did not carry it would answer
+// 401, Pair would read that as a card that is busy, and every turn would fall
+// back to the resident model with nothing in the log naming why.
+func TestPairSignsTheProbeAndTheCompletion(t *testing.T) {
+	seen := make(chan string, 2)
+	srv := httptest.NewServer(http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		seen <- r.Header.Get("Authorization")
+		if r.URL.Path == "/health" {
+			return
+		}
+		_, _ = w.Write([]byte(`{"choices":[{"message":{"content":"ok"}}]}`))
+	}))
+	defer srv.Close()
+
+	remote := New(srv.URL, time.Second)
+	remote.SetToken("s3cret")
+	p := NewPair(remote, New(srv.URL, time.Second), srv.URL+"/health", time.Hour)
+	p.probe(context.Background())
+	if !p.Available() {
+		t.Fatal("the probe did not admit an answering workstation")
+	}
+	if _, err := p.Complete(context.Background(), Req{User: "привет"}); err != nil {
+		t.Fatalf("complete: %v", err)
+	}
+	for i := 0; i < 2; i++ {
+		if got := <-seen; got != "Bearer s3cret" {
+			t.Errorf("request %d carried %q, want the bearer token", i, got)
+		}
+	}
+}