docs: add Choosing a Database comparison guide

[coji]

Summary

• New guide: website/guide/databases.md
• Covers all 5 backends: libSQL, Turso, better-sqlite3, PostgreSQL, SQLocal
• Comparison table, decision flowchart, setup code, trade-offs
• Added to sidebar under Introduction

Closes #112

Test plan

• pnpm validate passes
• Preview site to verify rendering

🤖 Generated with Claude Code

Summary by CodeRabbit

リリースノート

• ドキュメント
  • サイドバーに新しいガイド「データベースの選択」を追加しました
  • 複数のデータベースバックエンド（libSQL、Turso、better-sqlite3、PostgreSQL、SQLocalなど）の選択ガイドを含む包括的なドキュメントを提供します。セットアップ手順、コード例、各バックエンドの詳細情報が含まれています

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: e7b90bd9-c802-4a57-9369-d842967db5e1

📥 Commits

Reviewing files that changed from the base of the PR and between 3a5f4b7 and 25d4d51.

📒 Files selected for processing (1)

• website/guide/databases.md

📝 Walkthrough

Walkthrough

VitePressサイドバーナビゲーションに新しい「データベースの選択」ガイド項目を追加し、複数のデータベースバックエンド（libSQL、Turso、better-sqlite3、PostgreSQL、SQLocal）の比較と選択フローを説明する包括的なドキュメントページを新規作成しました。

Changes

コホート / ファイル	概要
サイドバーナビゲーション設定 website/.vitepress/config.ts	Introduction セクション内にサイドバー項目 { text: 'Choosing a Database', link: '/guide/databases' } を追加。
データベース選択ガイド website/guide/databases.md	新規ドキュメントファイルを作成。複数のデータベースバックエンドの特性（libSQL、Turso、better-sqlite3、PostgreSQL、SQLocal）、セットアップコマンド、TypeScript例、意思決定フロー、SQLiteバックエンドの単一ライター制限に関する注記を含む。

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~12 minutes

Poem

🐰 データベースの迷宮も案内書あれば明るい
SQLite か PostgreSQL か Turso か
選択の樹々を照らす新しき光
ドキュメント仲間たちが喜ぶ姿が見える 🌟

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately describes the main change: adding a comprehensive comparison guide for database selection.
Linked Issues check	✅ Passed	The PR addresses issue #112 by adding the databases.md guide with comparison content and updating the sidebar configuration as required.
Out of Scope Changes check	✅ Passed	All changes are directly aligned with the linked issue requirements. Only the guide file and sidebar entry were added, with no extraneous modifications.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch docs/choosing-database

📝 Coding Plan

• Generate coding plan for human review comments

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[coderabbitai]

Actionable comments posted: 2

🤖 Prompt for all review comments with AI agents

Verify each finding against the current code and only fix it if needed.

Inline comments:
In `@website/guide/databases.md`:
- Around line 7-13: The comparison table is missing the requested axes; add
three new columns titled "Performance", "Cost", and "Serverless compatibility"
to the existing header row and update every backend row (libSQL, Turso,
better-sqlite3, PostgreSQL, SQLocal) to include concise values for those columns
(e.g., "low/medium/high" or short phrases like "good/poor", and
"yes/no/limited") matching the table's pipe-separated Markdown format so the
table remains aligned with the existing "Workers" and "Setup" columns and the
Issue `#112` acceptance criteria.
- Line 83: 「For CLI tools and scripts. Lightweight synchronous SQLite with no
native dependencies on most
platforms.」の記述が誤りです。better-sqlite3はネイティブアドオンであり、プリビルドバイナリが利用できない環境ではビルドツール（例:
Python、C/C++コンパイラ、make 等）が必要になる旨に文章を修正してください（参照箇所:本文中の "better-sqlite3"
と前述の文言を置き換える）。

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 5880f338-f354-47f9-bfdd-8798f5c90666

📥 Commits

Reviewing files that changed from the base of the PR and between 4f84aa5 and 3a5f4b7.

📒 Files selected for processing (2)

• website/.vitepress/config.ts
• website/guide/databases.md