feat: add livestreams page with every FCAIC episode

[esrakadah]

Adds a /livestreams page that lists every FCAIC episode from the YouTube playlist, so the site has a proper archive instead of a single "Past Livestream" card.

What's in it

• New route /livestreams: the latest episode featured on top, the rest grouped by year in a grid, plus a search over episode number and topic. Hero shows episode count, total hours live and the start month, with "Watch the playlist" and "Pitch a topic" buttons. "Pitch a topic" goes to the FCAIC Sessionize page (https://sessionize.com/fcaic).
• Linked from the navbar (after Builders) and the footer (Resources).
• Generated data: tool/fetch_livestreams.dart reads the playlist and each stream's start date (Europe/Berlin) and writes lib/src/data/livestreams.g.dart. No new dependencies. After each stream:

  dart run tool/fetch_livestreams.dart

  The README has the same note.

Relation to #8

Both this PR and #8 add a sessionizeCallForSpeakers entry to ExternalLink, so whichever merges second gets a small conflict in external_links.dart. To fix it, keep one entry, and keep buildWithAI2026 if #8 still has it. Nothing else overlaps. I left the home page "Past Livestream" card untouched on purpose because #8 changes those lines. Once #8 lands, that card can point to /livestreams, which is a one-line follow-up and covers Stef's "Past Livestreams" request.

Checked

• dart format --line-length=100 and dart analyze are clean (only the two existing infos remain).
• webdev build works. Tested locally on desktop and at 375px with no horizontal scroll and no console errors. Search tested with multi-word queries and with no results.
• All 29 episode dates cross-checked against an independent list.

🤖 Generated with Claude Code

[github-actions]

Visit the preview URL for this PR (updated for commit b4b1fa2):

https://flutter-community-ai--pr10-feat-livestreams-pag-ppo9w3uv.web.app

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