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>

crates/punktfunk-host/src/vdisplay/windows/manager.rs

@@ -31,7 +31,7 @@ use windows::Win32::System::Threading::{
     CreateMutexW, OpenProcess, WaitForSingleObject, PROCESS_SYNCHRONIZE,
 };
 
-use super::{Mode, VirtualOutput};
+use super::{DisplayOwnership, Mode, VirtualOutput};
 use crate::win_display::{
     force_extend_topology, isolate_displays_ccd, resolve_gdi_name, restore_displays_ccd,
     set_active_mode, set_virtual_primary_ccd, SavedConfig,
@@ -531,6 +531,9 @@ impl VirtualDisplayManager {
                 mgr: self,
                 gen: mon.gen,
             }),
+            // The Windows manager owns the monitor lifecycle (refcount/linger/pin), so the registry
+            // (which delegates to it via `vd.create`) treats it as Owned.
+            ownership: DisplayOwnership::Owned,
         }
     }