feat(lobby): F8-04b hierarchical sidebar + paid-tier gate for create-game

Reshape the lobby UI from a single Overview into a two-level sidebar
(games · profile · DEV synthetic-reports) with four games sub-panels
(active-past · recruitment · invitations · private-games). Move the
`create new game` button into the private-games panel, merge the
applications section into recruitment cards as status chips, and add
DEV-only synthetic-report loader as a top-level screen.

Add a paid-tier gate at backend `lobby.game.create`: free callers get
`403 forbidden` before the lobby service is invoked. The UI hides the
private-games sub-panel + create button on free tier (DEV affordances
flag overrides). Update every integration test that creates a game to
use a new `testenv.PromoteToPaid` helper; add a new
`TestLobbyFlow_FreeUserCreateGameForbidden`.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

ui/frontend/src/lib/i18n/locales/en.ts

@@ -55,16 +55,31 @@ const en = {
 	"lobby.nav.aria_label": "lobby pages",
 	"lobby.nav.overview": "Overview",
 	"lobby.nav.profile": "Profile",
+	"lobby.nav.games": "games",
+	"lobby.nav.games.active_past": "active & past",
+	"lobby.nav.games.recruitment": "recruitment",
+	"lobby.nav.games.invitations": "invitations",
+	"lobby.nav.games.private_games": "private games",
+	"lobby.nav.games.aria_label": "games sections",
+	"lobby.nav.games.mobile_toggle": "games · {label}",
+	"lobby.nav.synthetic_reports": "Synthetic test reports",
 	"lobby.section.my_games": "my games",
 	"lobby.section.invitations": "pending invitations",
 	"lobby.section.applications": "my applications",
 	"lobby.section.public_games": "public games",
+	"lobby.section.recruitment": "open recruitment",
+	"lobby.section.private_games": "my private games",
 	"lobby.section.create": "create a game",
 	"lobby.create_button": "create new game",
 	"lobby.my_games.empty": "no games yet",
 	"lobby.invitations.empty": "no invitations",
 	"lobby.applications.empty": "no applications",
 	"lobby.public_games.empty": "no public games",
+	"lobby.games.active_past.empty": "no active or past games",
+	"lobby.games.private_games.empty": "no private games yet",
+	"lobby.recruitment.empty": "no open recruitment",
+	"lobby.recruitment.applied_pending": "your application is awaiting approval",
+	"lobby.recruitment.applied_approved": "your application was accepted",
 	"lobby.invitation.accept": "accept",
 	"lobby.invitation.decline": "decline",
 	"lobby.application.submit": "submit application",
@@ -96,6 +111,8 @@ const en = {
 	"lobby.create.game_name_required": "game name must not be empty",
 	"lobby.create.turn_schedule_required": "turn schedule must not be empty",
 	"lobby.create.enrollment_ends_at_required": "enrollment end time must be set",
+	"lobby.create.error.forbidden":
+		"Game creation is available only on a paid plan.",
 	"lobby.error.invalid_request": "request is invalid",
 	"lobby.error.subject_not_found": "not found",
 	"lobby.error.forbidden": "operation is forbidden",