Overhaul Flutter installation docs and simplify site navigation

[conooi]

Description of what this PR is changing or adding, and why:

This PR streamlines the Flutter installation documentation and site navigation to make it easier for both new and returning developers to find the right setup path:

• Consolidate /install and /install/custom onto /install:
  • Replaces the multi-hop routing flow with a single Install and set up Flutter hub at /install featuring two side-by-side installation options right at the top: Install with VS Code (/install/quick) and Download and install manually (/install/manual).
  • Includes scannable links for configuring target platforms (Android, iOS, web, Windows, macOS, Linux), setting up editors/IDEs, and managing or troubleshooting an existing Flutter SDK installation.
  • Removes sites/docs/src/content/install/custom.md and redirects /install/custom and /get-started/custom to /install.
• Consolidate /install/quick and /install/with-vs-code onto /install/quick:
  • Merges Code OSS-based editor guidance and the flutter doctor validation step from with-vs-code.md into /install/quick (Install Flutter with VS Code).
  • Removes the redundant Test drive Flutter tutorial section from the install page so installation and learning (/learn/pathway) are clearly separated.
  • Enables sitemap indexing on /install/quick, removes with-vs-code.md, and redirects /install/with-vs-code to /install/quick.
• Polish /install/manual and unify next-steps cards:
  • Simplifies the SDK archive extraction examples across Windows, macOS, and Linux/ChromeOS.
  • Adds a Validate your setup (flutter doctor) section with guidance on expected checkmarks.
  • Reuses the setup-next-steps.html partial across both /install/quick and /install/manual (with OS-filtered target platform links and a direct link to Create a new Flutter app).
• Simplify navigation and header:
  • Removes the top-right Get started CTA button from the docs.flutter.dev header.
  • Simplifies the top Get started sidenav section to Install Flutter (/install/quick) and Learn Flutter (/learn), and lists Overview (/install), Install with VS Code (/install/quick), and Install manually (/install/manual) under Manage install.

Issues fixed by this PR (if any):

Fixes #13540
Supersedes #13959

[flutter-website-bot]

Staged preview of the updated docs.flutter.dev site (updated for commit ee465b5):

https://flutter-docs-prod--docs-pr13982-install-page-overhaul-c0wlihsv.web.app

[gemini-code-assist]

Code Review

This pull request restructures the Flutter installation documentation by consolidating the setup paths into a recommended "Install with VS Code" flow and a manual installation flow. It updates the main installation overview page, simplifies SDK extraction instructions, and updates sidenav links and redirects. The review feedback correctly identifies that the link to "Antigravity" is an internal Google-only resource and suggests replacing it with "VSCodium" to ensure public accessibility.

[flutter-website-bot]

Staged preview of the updated flutter.dev site (updated for commit ce777f2):

https://flutter-dev-230821--www-pr13982-install-page-overhaul-97b8bdwy.web.app