Stage 17 round 6 (#16/#17, PR C): lobby sort + server-derived in-game friend state

Lobby: group the my-games list into your-turn / opponent-turn / finished
(empty sections hidden), ordered by last activity (your-turn oldest-first,
the other two newest-first), as a compact line-separated list. gameDTO and
FB GameView gain last_activity_unix (turn start while active, finish time
once finished); a pure lib/lobbysort.ts holds the grouping/ordering.

Friends: the in-game 'add to friends' item is now server-derived via a new
GET /user/friends/outgoing (+ friends.outgoing op), returning addressees with
a pending OR declined request (both read as 'request sent'), so it is correct
across reloads; it shows a disabled '✓ in friends' once accepted. It
live-updates when the opponent answers: RespondFriendRequest now publishes
friend_added (accept) / friend_declined (new notify sub-kind, decline) to the
original requester, whose open game re-derives its friend state.

Tests: lobbysort unit test; gateway outgoing + last_activity transcode tests;
backend integration ListOutgoingRequests + respond-publishes-to-requester;
e2e updated for the new lobby section labels + a non-friend active opponent.
Docs: ARCHITECTURE notify catalog, FUNCTIONAL(+ru) lobby/friends, PLAN.

backend/internal/inttest/social_test.go

@@ -6,6 +6,7 @@ import (
 	"context"
 	"errors"
 	"strings"
+	"sync"
 	"testing"
 	"time"
 
@@ -14,9 +15,36 @@ import (
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/game"
+	"scrabble/backend/internal/notify"
 	"scrabble/backend/internal/social"
+	fb "scrabble/pkg/fbs/scrabblefb"
 )
 
+// capturePublisher records every published intent for assertions on live events.
+type capturePublisher struct {
+	mu      sync.Mutex
+	intents []notify.Intent
+}
+
+func (c *capturePublisher) Publish(in ...notify.Intent) {
+	c.mu.Lock()
+	defer c.mu.Unlock()
+	c.intents = append(c.intents, in...)
+}
+
+// notified reports whether a Notification with the given sub-kind was published to user.
+func (c *capturePublisher) notified(user uuid.UUID, sub string) bool {
+	c.mu.Lock()
+	defer c.mu.Unlock()
+	for _, in := range c.intents {
+		if in.UserID == user && in.Kind == notify.KindNotification &&
+			string(fb.GetRootAsNotificationEvent(in.Payload, 0).Kind()) == sub {
+			return true
+		}
+	}
+	return false
+}
+
 // newSocialService builds a social service over the shared pool, reading game
 // state through a real game service.
 func newSocialService() *social.Service {
@@ -383,3 +411,93 @@ func TestNudgeCooldownResetsOnAction(t *testing.T) {
 		t.Fatalf("nudge after acting = %v, want allowed (cooldown reset)", err)
 	}
 }
+
+// TestListOutgoingRequests checks the requester-side list that backs the in-game "add to
+// friends" item (Stage 17): a pending request shows for the requester only; an accepted one
+// clears (it is a friendship now); a declined one stays (cannot be re-sent, so it reads as
+// still "sent"); a lazily expired pending one drops (it may be re-sent).
+func TestListOutgoingRequests(t *testing.T) {
+	ctx := context.Background()
+	svc := newSocialService()
+
+	// Pending: outgoing for the requester, not the addressee.
+	_, s1 := newGameWithSeats(t, 2)
+	a, b := s1[0], s1[1]
+	if err := svc.SendFriendRequest(ctx, a, b); err != nil {
+		t.Fatalf("send: %v", err)
+	}
+	if got, _ := svc.ListOutgoingRequests(ctx, a); len(got) != 1 || got[0] != b {
+		t.Fatalf("outgoing pending = %v, want [b]", got)
+	}
+	if got, _ := svc.ListOutgoingRequests(ctx, b); len(got) != 0 {
+		t.Fatalf("addressee outgoing = %v, want none", got)
+	}
+	// Accepted: a friendship, no longer an outgoing request.
+	if err := svc.RespondFriendRequest(ctx, b, a, true); err != nil {
+		t.Fatalf("accept: %v", err)
+	}
+	if got, _ := svc.ListOutgoingRequests(ctx, a); len(got) != 0 {
+		t.Fatalf("outgoing after accept = %v, want none", got)
+	}
+
+	// Declined: stays outgoing (reads as sent; cannot re-send).
+	_, s2 := newGameWithSeats(t, 2)
+	c, d := s2[0], s2[1]
+	if err := svc.SendFriendRequest(ctx, c, d); err != nil {
+		t.Fatalf("send2: %v", err)
+	}
+	if err := svc.RespondFriendRequest(ctx, d, c, false); err != nil {
+		t.Fatalf("decline: %v", err)
+	}
+	if got, _ := svc.ListOutgoingRequests(ctx, c); len(got) != 1 || got[0] != d {
+		t.Fatalf("outgoing after decline = %v, want [d]", got)
+	}
+
+	// Lazily expired pending: omitted (may be re-sent).
+	_, s3 := newGameWithSeats(t, 2)
+	e, f := s3[0], s3[1]
+	if err := svc.SendFriendRequest(ctx, e, f); err != nil {
+		t.Fatalf("send3: %v", err)
+	}
+	if _, err := testDB.ExecContext(ctx,
+		`UPDATE backend.friendships SET created_at = now() - interval '31 days' WHERE requester_id = $1 AND addressee_id = $2`, e, f); err != nil {
+		t.Fatalf("backdate: %v", err)
+	}
+	if got, _ := svc.ListOutgoingRequests(ctx, e); len(got) != 0 {
+		t.Fatalf("expired outgoing = %v, want none", got)
+	}
+}
+
+// TestRespondPublishesToRequester checks that answering a request notifies the original
+// requester over the live channel (Stage 17): accept -> friend_added, decline ->
+// friend_declined, so a game screen watching that opponent re-derives its friend state.
+func TestRespondPublishesToRequester(t *testing.T) {
+	ctx := context.Background()
+	svc := newSocialService()
+	pub := &capturePublisher{}
+	svc.SetNotifier(pub)
+
+	_, s1 := newGameWithSeats(t, 2)
+	a, b := s1[0], s1[1]
+	if err := svc.SendFriendRequest(ctx, a, b); err != nil {
+		t.Fatalf("send: %v", err)
+	}
+	if err := svc.RespondFriendRequest(ctx, b, a, true); err != nil {
+		t.Fatalf("accept: %v", err)
+	}
+	if !pub.notified(a, notify.NotifyFriendAdded) {
+		t.Errorf("accept did not notify requester with %q", notify.NotifyFriendAdded)
+	}
+
+	_, s2 := newGameWithSeats(t, 2)
+	c, d := s2[0], s2[1]
+	if err := svc.SendFriendRequest(ctx, c, d); err != nil {
+		t.Fatalf("send2: %v", err)
+	}
+	if err := svc.RespondFriendRequest(ctx, d, c, false); err != nil {
+		t.Fatalf("decline: %v", err)
+	}
+	if !pub.notified(c, notify.NotifyFriendDeclined) {
+		t.Errorf("decline did not notify requester with %q", notify.NotifyFriendDeclined)
+	}
+}