Reduce code duplication and update README

- Extract shared utilities (HIDDEN_FILES, VIDEO_EXTENSIONS, fileApiUrl,
  thumbnailApiUrl, findFile) into new src/lib/media-utils.ts, removing
  identical copies from games.ts, movies.ts, tv.ts, files.ts, and scanner.ts
- Add comment in files.ts clarifying why its VIDEO_EXTENSIONS set intentionally
  differs from the media library set (web-playable formats for the mixed browser)
- Rewrite README to reflect the current feature set: Movies/TV libraries, auth
  system, tag system, background scanner, updated project structure, folder
  conventions for all four library types, and a complete API reference

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/lib/games.ts

@@ -1,33 +1,7 @@
 import fs from 'fs'
 import path from 'path'
 import type { Game, GameSeries } from '@/types'
-
-const HIDDEN_FILES = /^\./
-
-/**
- * Finds the first file in a directory whose basename (without extension)
- * matches the given pattern (case-insensitive).
- */
-function findFile(dir: string, pattern: RegExp): string | null {
-  let entries: string[]
-  try {
-    entries = fs.readdirSync(dir)
-  } catch {
-    return null
-  }
-  const match = entries.find(
-    (entry) => !HIDDEN_FILES.test(entry) && pattern.test(path.basename(entry, path.extname(entry)))
-  )
-  return match ?? null
-}
-
-function fileApiUrl(libraryId: string, relativePath: string): string {
-  return `/api/file?libraryId=${encodeURIComponent(libraryId)}&path=${encodeURIComponent(relativePath)}`
-}
-
-function thumbnailApiUrl(libraryId: string, relativePath: string): string {
-  return `/api/thumbnail?libraryId=${encodeURIComponent(libraryId)}&path=${encodeURIComponent(relativePath)}`
-}
+import { HIDDEN_FILES, fileApiUrl, thumbnailApiUrl, findFile } from './media-utils'
 
 /**
  * Attempts to build a Game from a directory.