feat: Playnite library sync plugin + exporter

A two-part Punktfunk plugin that syncs the Playnite library into the host
game library as the `playnite` provider:

- exporter/ — a minimal C# Playnite GenericPlugin ("Punktfunk Sync") that
  writes punktfunk-library.json on every library change. Reading Playnite's
  live-locked LiteDB from outside isn't robust, so this adapter runs inside
  Playnite. Builds net462 via reference assemblies; packaged as a .pext.
- src/ — the TS plugin (on @punktfunk/host, rom-manager shape): watches the
  export, embeds covers as data URLs, reconciles via
  PUT /library/provider/playnite, with a console-hosted web UI + standalone
  fallback + CLI. Launch = playnite://playnite/start/<id>, run by the host
  in the interactive session so Playnite performs the real launch.

Verified locally: backend tsc + 23 tests + biome clean, SPA build, C#
exporter build + .pext pack.

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

exporter/Model.cs

@@ -0,0 +1,68 @@
+using System.Collections.Generic;
+using Playnite.SDK.Data;
+
+namespace PunktfunkSync
+{
+    // The on-disk contract with the Punktfunk `playnite` plugin. Keep these property names in lockstep
+    // with `src/export-schema.ts` (ExportedGame / LibraryExport). Serialized via the Playnite SDK's
+    // `Serialization.ToJson`, so `[SerializationPropertyName]` pins the JSON keys regardless of the
+    // serializer's default casing.
+
+    public class ExportedGame
+    {
+        // Playnite's stable game Guid ("d"-format, lowercase with dashes) — the reconcile external_id.
+        [SerializationPropertyName("id")]
+        public string Id { get; set; }
+
+        [SerializationPropertyName("name")]
+        public string Name { get; set; }
+
+        [SerializationPropertyName("installed")]
+        public bool Installed { get; set; }
+
+        [SerializationPropertyName("hidden")]
+        public bool Hidden { get; set; }
+
+        // Library source name ("Steam", "GOG", "Epic", emulator name…) or null.
+        [SerializationPropertyName("source")]
+        public string Source { get; set; }
+
+        [SerializationPropertyName("platforms")]
+        public List<string> Platforms { get; set; }
+
+        // ABSOLUTE paths on the host box (already resolved from Playnite's database-relative form), or
+        // null. A remote (http) art URL is passed through verbatim.
+        [SerializationPropertyName("cover")]
+        public string Cover { get; set; }
+
+        [SerializationPropertyName("background")]
+        public string Background { get; set; }
+
+        [SerializationPropertyName("icon")]
+        public string Icon { get; set; }
+    }
+
+    public class PlayniteInfo
+    {
+        [SerializationPropertyName("version")]
+        public string Version { get; set; }
+
+        [SerializationPropertyName("mode")]
+        public string Mode { get; set; }
+    }
+
+    public class LibraryExport
+    {
+        [SerializationPropertyName("schema")]
+        public int Schema { get; set; }
+
+        [SerializationPropertyName("generatedAt")]
+        public string GeneratedAt { get; set; }
+
+        [SerializationPropertyName("playnite")]
+        public PlayniteInfo Playnite { get; set; }
+
+        [SerializationPropertyName("games")]
+        public List<ExportedGame> Games { get; set; }
+    }
+}