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>

biome.json

@@ -0,0 +1,51 @@
+{
+	"$schema": "https://biomejs.dev/schemas/2.5.4/schema.json",
+	"vcs": {
+		"enabled": true,
+		"clientKind": "git",
+		"useIgnoreFile": true
+	},
+	"files": {
+		"ignoreUnknown": false,
+		"includes": ["**", "!dist", "!ui/dist", "!**/node_modules", "!exporter"]
+	},
+	"formatter": {
+		"enabled": true,
+		"indentStyle": "tab"
+	},
+	"css": {
+		"parser": {
+			"tailwindDirectives": true
+		}
+	},
+	"assist": {
+		"actions": {
+			"source": {
+				"organizeImports": "on"
+			}
+		}
+	},
+	"linter": {
+		"enabled": true,
+		"rules": {
+			"preset": "recommended",
+			"suspicious": {
+				"noArrayIndexKey": "off"
+			},
+			"style": {
+				"noNonNullAssertion": "off"
+			},
+			"a11y": {
+				"noLabelWithoutControl": "off"
+			},
+			"correctness": {
+				"useExhaustiveDependencies": "warn"
+			}
+		}
+	},
+	"javascript": {
+		"formatter": {
+			"quoteStyle": "double"
+		}
+	}
+}