Add search box to tutorial left navigation

[CamSoper]

Problem

The tutorials section currently lacks a search box in its left navigation, while the main docs navigation now includes one.

Proposal

Add the same search box component to the tutorial left navigation that was added to the docs navigation in the recent navigation reorganization.

Implementation Details

The search box should:

• Be placed at the top of the left navigation in tutorial pages
• Use the same docs-search component as the docs pages
• Include the conditional placeholder for local development without Algolia credentials
• Match the styling and spacing of the docs navigation search box

Reference

See /workspaces/src/pulumi/docs/layouts/partials/docs/menu.html (lines 52-69) for the implementation pattern to follow.

The tutorial navigation would need similar updates to:

• Add the search component at the top of the nav
• Ensure proper Tailwind styling is applied
• Include the conditional {{ if getenv "ALGOLIA_APP_ID" }} logic

Acceptance Criteria

• Search box appears at top of tutorial left navigation
• Search box has same styling as docs navigation
• Placeholder shows in dev without Algolia credentials
• Real search works in production with credentials
• No visual regressions in tutorial navigation