refactor: extract gametime package, replace fmt.Printf with zap logging

Move time utilities (TimeAdjusted, TimeMidnight, TimeWeekStart, TimeWeekNext,
TimeGameAbsolute) from channelserver into common/gametime to break the
inappropriate dependency where signserver, entranceserver, and api imported
the 38K-line channelserver package just for time functions.

Replace all fmt.Printf debug logging in sys_session.go and handlers_object.go
with structured zap logging for consistent observability.

common/gametime/gametime_test.go

@@ -0,0 +1,157 @@
+package gametime
+
+import (
+	"testing"
+	"time"
+)
+
+func TestAdjusted(t *testing.T) {
+	result := Adjusted()
+
+	_, offset := result.Zone()
+	expectedOffset := 9 * 60 * 60
+	if offset != expectedOffset {
+		t.Errorf("Adjusted() zone offset = %d, want %d (UTC+9)", offset, expectedOffset)
+	}
+
+	now := time.Now()
+	diff := result.Sub(now.In(time.FixedZone("UTC+9", 9*60*60)))
+	if diff < -time.Second || diff > time.Second {
+		t.Errorf("Adjusted() time differs from expected by %v", diff)
+	}
+}
+
+func TestMidnight(t *testing.T) {
+	midnight := Midnight()
+
+	if midnight.Hour() != 0 {
+		t.Errorf("Midnight() hour = %d, want 0", midnight.Hour())
+	}
+	if midnight.Minute() != 0 {
+		t.Errorf("Midnight() minute = %d, want 0", midnight.Minute())
+	}
+	if midnight.Second() != 0 {
+		t.Errorf("Midnight() second = %d, want 0", midnight.Second())
+	}
+	if midnight.Nanosecond() != 0 {
+		t.Errorf("Midnight() nanosecond = %d, want 0", midnight.Nanosecond())
+	}
+
+	_, offset := midnight.Zone()
+	expectedOffset := 9 * 60 * 60
+	if offset != expectedOffset {
+		t.Errorf("Midnight() zone offset = %d, want %d (UTC+9)", offset, expectedOffset)
+	}
+}
+
+func TestWeekStart(t *testing.T) {
+	weekStart := WeekStart()
+
+	if weekStart.Weekday() != time.Monday {
+		t.Errorf("WeekStart() weekday = %v, want Monday", weekStart.Weekday())
+	}
+
+	if weekStart.Hour() != 0 || weekStart.Minute() != 0 || weekStart.Second() != 0 {
+		t.Errorf("WeekStart() should be at midnight, got %02d:%02d:%02d",
+			weekStart.Hour(), weekStart.Minute(), weekStart.Second())
+	}
+
+	_, offset := weekStart.Zone()
+	expectedOffset := 9 * 60 * 60
+	if offset != expectedOffset {
+		t.Errorf("WeekStart() zone offset = %d, want %d (UTC+9)", offset, expectedOffset)
+	}
+
+	midnight := Midnight()
+	if weekStart.After(midnight) {
+		t.Errorf("WeekStart() %v should be <= current midnight %v", weekStart, midnight)
+	}
+}
+
+func TestWeekNext(t *testing.T) {
+	weekStart := WeekStart()
+	weekNext := WeekNext()
+
+	expectedNext := weekStart.Add(time.Hour * 24 * 7)
+	if !weekNext.Equal(expectedNext) {
+		t.Errorf("WeekNext() = %v, want %v (7 days after WeekStart)", weekNext, expectedNext)
+	}
+
+	if weekNext.Weekday() != time.Monday {
+		t.Errorf("WeekNext() weekday = %v, want Monday", weekNext.Weekday())
+	}
+
+	if weekNext.Hour() != 0 || weekNext.Minute() != 0 || weekNext.Second() != 0 {
+		t.Errorf("WeekNext() should be at midnight, got %02d:%02d:%02d",
+			weekNext.Hour(), weekNext.Minute(), weekNext.Second())
+	}
+
+	if !weekNext.After(weekStart) {
+		t.Errorf("WeekNext() %v should be after WeekStart() %v", weekNext, weekStart)
+	}
+}
+
+func TestWeekStartSundayEdge(t *testing.T) {
+	weekStart := WeekStart()
+
+	if weekStart.Weekday() != time.Monday {
+		t.Errorf("WeekStart() on any day should return Monday, got %v", weekStart.Weekday())
+	}
+}
+
+func TestMidnightSameDay(t *testing.T) {
+	adjusted := Adjusted()
+	midnight := Midnight()
+
+	if midnight.Year() != adjusted.Year() ||
+		midnight.Month() != adjusted.Month() ||
+		midnight.Day() != adjusted.Day() {
+		t.Errorf("Midnight() date = %v, want same day as Adjusted() %v",
+			midnight.Format("2006-01-02"), adjusted.Format("2006-01-02"))
+	}
+}
+
+func TestWeekDuration(t *testing.T) {
+	weekStart := WeekStart()
+	weekNext := WeekNext()
+
+	duration := weekNext.Sub(weekStart)
+	expectedDuration := time.Hour * 24 * 7
+
+	if duration != expectedDuration {
+		t.Errorf("Duration between WeekStart and WeekNext = %v, want %v", duration, expectedDuration)
+	}
+}
+
+func TestTimeZoneConsistency(t *testing.T) {
+	adjusted := Adjusted()
+	midnight := Midnight()
+	weekStart := WeekStart()
+	weekNext := WeekNext()
+
+	times := []struct {
+		name string
+		time time.Time
+	}{
+		{"Adjusted", adjusted},
+		{"Midnight", midnight},
+		{"WeekStart", weekStart},
+		{"WeekNext", weekNext},
+	}
+
+	expectedOffset := 9 * 60 * 60
+	for _, tt := range times {
+		_, offset := tt.time.Zone()
+		if offset != expectedOffset {
+			t.Errorf("%s() zone offset = %d, want %d (UTC+9)", tt.name, offset, expectedOffset)
+		}
+	}
+}
+
+func TestGameAbsolute(t *testing.T) {
+	result := GameAbsolute()
+
+	if result >= 5760 {
+		t.Errorf("GameAbsolute() = %d, should be < 5760", result)
+	}
+}