refactor(api): separate business logic into game, tournament, session packages

Extract business logic from api/handler.go into dedicated service packages:
- session: context helpers (resolves admin → api import dependency)
- game: game state, code submission, ranking, watch logic
- tournament: bracket construction and seed ordering
- api/convert.go: domain → API type conversion functions

api/handler.go is now a thin adapter that delegates to services and
maps domain errors to HTTP status codes.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

1 files changed, 82 insertions, 0 deletions

diff --git a/backend/game/service_test.go b/backend/game/service_test.go
new file mode 100644
index 0000000..95ceef6
--- /dev/null
+++ b/backend/game/service_test.go
@@ -0,0 +1,82 @@
+package game
+
+import (
+	"testing"
+	"time"
+
+	"github.com/jackc/pgx/v5/pgtype"
+)
+
+func TestIsGameRunning(t *testing.T) {
+	now := time.Now()
+	tests := []struct {
+		name            string
+		startedAt       pgtype.Timestamp
+		durationSeconds int32
+		want            bool
+	}{
+		{
+			name:            "not started",
+			startedAt:       pgtype.Timestamp{Valid: false},
+			durationSeconds: 300,
+			want:            false,
+		},
+		{
+			name:            "running",
+			startedAt:       pgtype.Timestamp{Time: now.Add(-1 * time.Minute), Valid: true},
+			durationSeconds: 300,
+			want:            true,
+		},
+		{
+			name:            "finished",
+			startedAt:       pgtype.Timestamp{Time: now.Add(-10 * time.Minute), Valid: true},
+			durationSeconds: 300,
+			want:            false,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := IsGameRunning(tt.startedAt, tt.durationSeconds)
+			if got != tt.want {
+				t.Errorf("IsGameRunning() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestIsGameFinished(t *testing.T) {
+	now := time.Now()
+	tests := []struct {
+		name            string
+		startedAt       pgtype.Timestamp
+		durationSeconds int32
+		want            bool
+	}{
+		{
+			name:            "not started",
+			startedAt:       pgtype.Timestamp{Valid: false},
+			durationSeconds: 300,
+			want:            false,
+		},
+		{
+			name:            "still running",
+			startedAt:       pgtype.Timestamp{Time: now.Add(-1 * time.Minute), Valid: true},
+			durationSeconds: 300,
+			want:            false,
+		},
+		{
+			name:            "finished",
+			startedAt:       pgtype.Timestamp{Time: now.Add(-10 * time.Minute), Valid: true},
+			durationSeconds: 300,
+			want:            true,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			got := IsGameFinished(tt.startedAt, tt.durationSeconds)
+			if got != tt.want {
+				t.Errorf("IsGameFinished() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}