feat(host): game-mode integration + dedicated game sessions

Implements design/gamemode-and-dedicated-sessions.md (Parts A1-A5 + B0-B2):
reconciles the merged display-management registry with session-mobile
Bazzite/SteamOS hosts and adds a per-launch dedicated gamescope mode.

- A1 DisplayOwnership {Owned,External,SessionManaged} + poolable_now(): the
  registry pools only what it owns, so gamescope managed/attach outputs are no
  longer double-owned by the registry AND the gamescope restore worker (fixes
  the game-mode-reconnect stale-node wedge).
- A2 validated reuse: (backend,mode,launch,epoch) reuse key + kept_display_alive
  liveness probe + reused_gen/mark_failed on a reused-display first-frame failure.
- A3 policy-driven managed restore (keep_alive replaces the hardcoded 5s debounce;
  forever = held = gaming-rig truthful) + crash-restore persist + SIGKILL teardown
  (kill_unit, applied to our transient unit AND the autologin stop -- validated
  live on .181 to avoid the F44 GPU-context leak).
- A4 session epoch: observe_session_instance bumps the epoch + invalidate_backend
  on a desktop-compositor instance change; gamescope spawns are exempt.
- A5 per-spawn log + PID-scoped gamescope node discovery.
- B0 game_session {auto,dedicated} policy (top-level, preset-orthogonal) +
  pick_gamescope_mode dedicated_launch + steam -silent command shaping.
- B1 free the autologin Steam before a dedicated Steam spawn (single-instance).
- B2 game-exit -> APP_EXITED_CLOSE_CODE (0x52) clean session end.

Adversarially reviewed (11 findings fixed). Validated on glass (.181 Bazzite F44,
RTX 4090): dedicated spawn streams a real game smoothly; keep-alive reuse; the
SIGKILL fix avoids the F44 vkCreateDevice leak. Workspace green
(build / test --workspace / clippy -D warnings / fmt), OpenAPI + C header
regenerated, web console tsc + vite build green. clients/probe: bump the
no-video timeout 8s->45s for gamescope cold starts.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

web/messages/de.json

@@ -97,6 +97,10 @@
 	"display_conflict_reject": "Besetzt — ablehnen",
 	"display_identity": "Client-Identität",
 	"display_identity_help": "Ob die gestreamte Anzeige eine stabile Client-Identität trägt, sodass der Desktop des Hosts die Monitor-Einstellungen dieses Clients (Skalierung, Auflösung) merkt und beim erneuten Verbinden wieder anwendet. Geteilt: eine Identität für alle. Pro Client: jedes Gerät eigene. Pro Client + Auflösung: separate Einstellungen je Gerät und Auflösung.",
+	"display_game_session": "Dedizierte Spiel-Sitzungen",
+	"display_game_session_help": "Wie eine Sitzung bedient wird, die ein Spiel aus der Bibliothek startet. „Dediziert“ gibt dem Start immer ein eigenes headless-gamescope in genau deiner Auflösung — das Spiel startet direkt, ohne Steam Big Picture, ohne Game-Mode. „Auto“ nutzt die aktuelle Sitzung der Box. gamescope muss installiert sein; sonst fällt Dediziert auf Auto zurück.",
+	"display_game_session_auto": "Auto",
+	"display_game_session_dedicated": "Dediziert",
 	"display_identity_shared": "Geteilt",
 	"display_identity_per_client": "Pro Client",
 	"display_identity_per_client_mode": "Pro Client + Auflösung",

web/messages/en.json

@@ -97,6 +97,10 @@
 	"display_conflict_reject": "Busy — reject",
 	"display_identity": "Per-client identity",
 	"display_identity_help": "Whether the streamed display carries a stable per-client identity, so the host's desktop remembers that client's per-monitor settings (scaling, resolution) and reapplies them when it reconnects. Shared: one identity for everyone. Per client: each device keeps its own. Per client + resolution: a device keeps separate settings per resolution it connects at.",
+	"display_game_session": "Dedicated game sessions",
+	"display_game_session_help": "How a session that launches a game from the library is served. “Dedicated” always gives the launch its own headless gamescope at your exact resolution — the game boots straight in, no Steam Big Picture, no game mode. “Auto” uses whatever session the box is in. gamescope must be installed; otherwise Dedicated falls back to Auto.",
+	"display_game_session_auto": "Auto",
+	"display_game_session_dedicated": "Dedicated",
 	"display_identity_shared": "Shared",
 	"display_identity_per_client": "Per client",
 	"display_identity_per_client_mode": "Per client + resolution",