Updates videos on docs landing page

[redbrogdon]

This PR swaps out the I/O embeds on our main page for three videos from the recent FlutterFlightPlans live stream.

[gemini-code-assist]

Summary of Changes

Hello @redbrogdon, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request updates the video section on the documentation landing page to feature more current and relevant content. It replaces older Google I/O 2025 video embeds with recent videos from the FlutterFlightPlans livestream, covering topics like Dart, Flutter, and GenUI. This change ensures that users visiting the page are presented with the latest educational and promotional video resources.

Highlights

• Video Content Update: The primary featured video on the documentation landing page has been updated to showcase 'What's New in Flutter 3.38 / Dart 3.10' from the FlutterFlightPlans livestream, replacing an older Google I/O 2025 video.
• Related Videos Refreshed: Two supplementary videos, previously related to Google I/O 2025, have been replaced with new content from FlutterFlightPlans, specifically 'Getting Started with GenUI' and 'How NotebookLM built a 4.8-Star Flutter app'.
• Introductory Text and Links: The descriptive text accompanying the video section and the associated external links have been updated to reflect the new FlutterFlightPlans series, ensuring consistency with the fresh video content.

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[gemini-code-assist]

Code Review

This pull request updates the embedded YouTube videos on the main documentation page to showcase recent content from the FlutterFlightPlans live stream. The changes are mostly content updates. I've found a couple of minor text issues, including a typo and some informal punctuation, and have provided suggestions to address them.

[flutter-website-bot]

Visit the preview URL for this PR (updated for commit b19ffe6):

https://flutter-docs-prod--pr12684-redbrogdon-patch-1-hw1qs6tz.web.app

[sfshaza2]

This looks great! thx!