feat(lifecycle): add AppMode type + DetectMode()

New pkg/lifecycle/mode.go introduces AppMode (Manager | Worker) and
DetectMode() that returns:
- Manager by default (explicit or empty env)
- Worker when CORE_APP_MODE=worker, or when empty env + CI=true signals
  a headless/compute context

Prerequisite for the BugSETI compute worker pattern (core/gui RFC.md §9.1) —
manager GUI runs the full app UI, workers run headless compute with only an
RPC surface.

Tests follow the core/go {Good,Bad,Ugly} naming convention; go test
./pkg/lifecycle/... passes.

Co-authored-by: Codex <noreply@openai.com>

Closes tasks.lthn.sh/view.php?id=32

pkg/lifecycle/mode.go

@@ -0,0 +1,52 @@
+package lifecycle
+
+import (
+	"os"
+	"strings"
+)
+
+type AppMode string
+
+const (
+	ModeManager AppMode = "manager"
+	ModeWorker  AppMode = "worker"
+)
+
+const (
+	appModeEnv = "CORE_APP_MODE"
+	ciEnv      = "CI"
+)
+
+// DetectMode returns ModeWorker when CORE_APP_MODE=worker.
+//
+//	mode := DetectMode()
+func DetectMode() AppMode {
+	if value, ok := os.LookupEnv(appModeEnv); ok {
+		if mode, valid := parseAppMode(value); valid {
+			return mode
+		}
+	}
+
+	if value, ok := os.LookupEnv(ciEnv); ok && isTrue(value) {
+		return ModeWorker
+	}
+
+	return ModeManager
+}
+
+func parseAppMode(value string) (AppMode, bool) {
+	switch strings.ToLower(strings.TrimSpace(value)) {
+	case string(ModeManager):
+		return ModeManager, true
+	case string(ModeWorker):
+		return ModeWorker, true
+	case "":
+		return "", false
+	default:
+		return ModeManager, true
+	}
+}
+
+func isTrue(value string) bool {
+	return strings.EqualFold(strings.TrimSpace(value), "true")
+}

pkg/lifecycle/mode_test.go

@@ -0,0 +1,57 @@
+package lifecycle
+
+import (
+	"os"
+	"testing"
+)
+
+func TestMode_DetectMode_Good(t *testing.T) {
+	unsetEnv(t, appModeEnv)
+	t.Setenv(ciEnv, "")
+
+	mode := DetectMode()
+	if mode != ModeManager {
+		t.Fatalf("expected manager mode, got %q", mode)
+	}
+}
+
+func TestMode_DetectMode_Bad(t *testing.T) {
+	t.Setenv(appModeEnv, "bogus")
+	t.Setenv(ciEnv, "")
+
+	mode := DetectMode()
+	if mode != ModeManager {
+		t.Fatalf("expected manager mode after invalid env value, got %q", mode)
+	}
+}
+
+func TestMode_DetectMode_Ugly(t *testing.T) {
+	t.Setenv(appModeEnv, "")
+	t.Setenv(ciEnv, "true")
+
+	mode := DetectMode()
+	if mode != ModeWorker {
+		t.Fatalf("expected worker mode in CI headless context, got %q", mode)
+	}
+}
+
+func unsetEnv(t *testing.T, key string) {
+	t.Helper()
+
+	value, ok := os.LookupEnv(key)
+	if err := os.Unsetenv(key); err != nil {
+		t.Fatalf("unset %s: %v", key, err)
+	}
+
+	t.Cleanup(func() {
+		if ok {
+			if err := os.Setenv(key, value); err != nil {
+				t.Fatalf("restore %s: %v", key, err)
+			}
+			return
+		}
+		if err := os.Unsetenv(key); err != nil {
+			t.Fatalf("restore unset %s: %v", key, err)
+		}
+	})
+}