chore: update docs, lib, and Rakefile for docs verification

- Update README files (en, ja, ko) with latest content
- Update editor docs (vscode, vim, neovim, syntax-highlighting)
- Enhance DocsExampleExtractor with improved extraction logic
- Enhance DocsExampleVerifier with better verification

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: yhk1038

README.ja.md

@@ -105,7 +105,7 @@ end
 - TypeScript のように、型がコードの中にあります。
 - `.trb` で書けば、`trc` が `.rb` と `.rbs` の両方を生成します。
 
-```ruby
+```trb
 # greet.trb
 def greet(name: String): String
   "Hello, #{name}!"
@@ -149,7 +149,7 @@ trc --version
 
 ### 1. `.trb` を書く
 
-```ruby
+```trb
 # hello.trb
 def greet(name: String): String
   "Hello, #{name}!"

README.ko.md

@@ -105,7 +105,7 @@ end
 - TypeScript처럼, 타입이 코드 안에 있습니다.
 - `.trb`로 작성하면 `trc`가 `.rb`와 `.rbs`를 모두 생성합니다.
 
-```ruby
+```trb
 # greet.trb
 def greet(name: String): String
   "Hello, #{name}!"
@@ -149,7 +149,7 @@ trc --version
 
 ### 1. `.trb` 작성
 
-```ruby
+```trb
 # hello.trb
 def greet(name: String): String
   "Hello, #{name}!"

README.md

@@ -110,7 +110,7 @@ end
 - Like TypeScript, types live inside your code.
 - Write `.trb`, and `trc` generates both `.rb` and `.rbs`.
 
-```ruby
+```trb
 # greet.trb
 def greet(name: String): String
   "Hello, #{name}!"
@@ -154,7 +154,7 @@ trc --version
 
 ### 1. Write `.trb`
 
-```ruby
+```trb
 # hello.trb
 def greet(name: String): String
   "Hello, #{name}!"

Rakefile

@@ -15,13 +15,24 @@ namespace :docs do
     verifier = TRuby::DocsExampleVerifier.new
 
     # Default patterns to check
+    # Includes both local docs and t-ruby.github.io documentation site
+    docs_site_path = "../t-ruby.github.io"
     patterns = [
       "docs/**/*.md",
       "README.md",
       "README.ja.md",
       "README.ko.md",
     ]
 
+    # Add t-ruby.github.io documentation if directory exists
+    if Dir.exist?(docs_site_path)
+      patterns += [
+        "#{docs_site_path}/docs/**/*.md",
+        "#{docs_site_path}/i18n/ko/docusaurus-plugin-content-docs/current/**/*.md",
+        "#{docs_site_path}/i18n/ja/docusaurus-plugin-content-docs/current/**/*.md",
+      ]
+    end
+
     puts "Verifying documentation examples..."
     puts
 
@@ -55,13 +66,22 @@ namespace :docs do
     verifier = TRuby::DocsExampleVerifier.new
     generator = TRuby::DocsBadgeGenerator.new
 
+    docs_site_path = "../t-ruby.github.io"
     patterns = [
       "docs/**/*.md",
       "README.md",
       "README.ja.md",
       "README.ko.md",
     ]
 
+    if Dir.exist?(docs_site_path)
+      patterns += [
+        "#{docs_site_path}/docs/**/*.md",
+        "#{docs_site_path}/i18n/ko/docusaurus-plugin-content-docs/current/**/*.md",
+        "#{docs_site_path}/i18n/ja/docusaurus-plugin-content-docs/current/**/*.md",
+      ]
+    end
+
     puts "Generating documentation coverage badge..."
 
     all_results = []
@@ -87,13 +107,22 @@ namespace :docs do
 
     extractor = TRuby::DocsExampleExtractor.new
 
+    docs_site_path = "../t-ruby.github.io"
     patterns = [
       "docs/**/*.md",
       "README.md",
       "README.ja.md",
       "README.ko.md",
     ]
 
+    if Dir.exist?(docs_site_path)
+      patterns += [
+        "#{docs_site_path}/docs/**/*.md",
+        "#{docs_site_path}/i18n/ko/docusaurus-plugin-content-docs/current/**/*.md",
+        "#{docs_site_path}/i18n/ja/docusaurus-plugin-content-docs/current/**/*.md",
+      ]
+    end
+
     all_examples = []
     patterns.each do |pattern|
       examples = extractor.extract_from_glob(pattern)

docs/neovim/en/getting-started.md

@@ -203,7 +203,7 @@ vim.api.nvim_create_autocmd("FileType", {
 
 1. Create `hello.trb`:
 
-```ruby
+```trb
 type UserId = String
 
 interface User

docs/neovim/ja/getting-started.md

@@ -203,7 +203,7 @@ vim.api.nvim_create_autocmd("FileType", {
 
 1. `hello.trb`を作成：
 
-```ruby
+```trb
 type UserId = String
 
 interface User

docs/neovim/ko/getting-started.md

@@ -203,7 +203,7 @@ vim.api.nvim_create_autocmd("FileType", {
 
 1. `hello.trb` 생성:
 
-```ruby
+```trb
 type UserId = String
 
 interface User

docs/syntax-highlighting/en/guide.md

@@ -19,15 +19,15 @@ T-Ruby syntax highlighting provides visual distinction for:
 
 ### Type Aliases
 
-```ruby
+```trb
 type UserId = String           # 'type' keyword, 'UserId' as type name
 type Age = Integer             # '=' operator, built-in type
 type UserMap = Hash<UserId, User>  # Generic type
 ```
 
 ### Interfaces
 
-```ruby
+```trb
 interface Printable            # 'interface' keyword, interface name
   to_string: String           # Member name, type annotation
   print: void
@@ -36,7 +36,7 @@ end                           # 'end' keyword
 
 ### Functions with Type Annotations
 
-```ruby
+```trb
 def greet(name: String): String    # Function name, param with type, return type
   "Hello, #{name}!"
 end
@@ -48,7 +48,7 @@ end
 
 ### Union and Intersection Types
 
-```ruby
+```trb
 type StringOrInt = String | Integer    # Union type with '|'
 type ReadWrite = Readable & Writable   # Intersection type with '&'
 type MaybeString = String | nil        # Nullable type
@@ -167,7 +167,7 @@ vim.api.nvim_create_autocmd("ColorScheme", {
 
 ### Simple Example
 
-```ruby
+```trb
 # simple.trb - Basic T-Ruby syntax
 
 type UserId = String
@@ -180,7 +180,7 @@ end
 
 ### Complex Example
 
-```ruby
+```trb
 # complex.trb - Advanced T-Ruby syntax
 
 type UserId = String

docs/syntax-highlighting/ja/guide.md

@@ -19,15 +19,15 @@ T-Rubyシンタックスハイライトは以下の要素を視覚的に区別
 
 ### 型エイリアス
 
-```ruby
+```trb
 type UserId = String           # 'type'キーワード、'UserId'を型名として
 type Age = Integer             # '='演算子、組み込み型
 type UserMap = Hash<UserId, User>  # ジェネリック型
 ```
 
 ### インターフェース
 
-```ruby
+```trb
 interface Printable            # 'interface'キーワード、インターフェース名
   to_string: String           # メンバー名、型アノテーション
   print: void
@@ -36,7 +36,7 @@ end                           # 'end'キーワード
 
 ### 型アノテーション付き関数
 
-```ruby
+```trb
 def greet(name: String): String    # 関数名、型付きパラメータ、戻り値型
   "こんにちは、#{name}さん！"
 end
@@ -48,7 +48,7 @@ end
 
 ### ユニオンとインターセクション型
 
-```ruby
+```trb
 type StringOrInt = String | Integer    # '|'を使ったユニオン型
 type ReadWrite = Readable & Writable   # '&'を使ったインターセクション型
 type MaybeString = String | nil        # Nullable型
@@ -167,7 +167,7 @@ vim.api.nvim_create_autocmd("ColorScheme", {
 
 ### シンプルな例
 
-```ruby
+```trb
 # simple.trb - 基本的なT-Ruby構文
 
 type UserId = String
@@ -180,7 +180,7 @@ end
 
 ### 複雑な例
 
-```ruby
+```trb
 # complex.trb - 高度なT-Ruby構文
 
 type UserId = String

docs/syntax-highlighting/ko/guide.md

@@ -19,15 +19,15 @@ T-Ruby 구문 강조는 다음 요소들을 시각적으로 구분합니다:
 
 ### 타입 별칭
 
-```ruby
+```trb
 type UserId = String           # 'type' 키워드, 'UserId' 타입명
 type Age = Integer             # '=' 연산자, 내장 타입
 type UserMap = Hash<UserId, User>  # 제네릭 타입
 ```
 
 ### 인터페이스
 
-```ruby
+```trb
 interface Printable            # 'interface' 키워드, 인터페이스명
   to_string: String           # 멤버명, 타입 어노테이션
   print: void
@@ -36,7 +36,7 @@ end                           # 'end' 키워드
 
 ### 타입 어노테이션이 있는 함수
 
-```ruby
+```trb
 def greet(name: String): String    # 함수명, 타입이 있는 매개변수, 반환 타입
   "안녕하세요, #{name}님!"
 end
@@ -48,7 +48,7 @@ end
 
 ### 유니온 및 인터섹션 타입
 
-```ruby
+```trb
 type StringOrInt = String | Integer    # '|'를 사용한 유니온 타입
 type ReadWrite = Readable & Writable   # '&'를 사용한 인터섹션 타입
 type MaybeString = String | nil        # Nullable 타입
@@ -167,7 +167,7 @@ vim.api.nvim_create_autocmd("ColorScheme", {
 
 ### 간단한 예제
 
-```ruby
+```trb
 # simple.trb - 기본 T-Ruby 구문
 
 type UserId = String
@@ -180,7 +180,7 @@ end
 
 ### 복잡한 예제
 
-```ruby
+```trb
 # complex.trb - 고급 T-Ruby 구문
 
 type UserId = String