Replace hardcoded suggestions with "popular actions" carousel

[twblack88]

Context

The three suggested actions above the prompt bar are hardcoded strings that don't represent the agent's actual capabilities. Replace them with a horizontally-scrolling carousel seeded from a curated popular-actions list.

Actions:

• Instantly Swap ETH for SOL
• Set a limit order
• Tell me about FOX
• Set up a TWAP/DCA into ETH
• What's my balance on Arbitrum?
• Check trending tokens
• Send some of my assets to another wallet

Files

• apps/agentic-chat/src/components/Chat.tsx:14-18 — current hardcoded suggestion array
• apps/agentic-chat/src/components/Chat.tsx:118-134 — current render (3 buttons)

Approach

• Add embla-carousel-react (~10KB, tree-shakeable — no shadcn carousel installed yet).
• Replace the 3-button grid with a horizontally-scrolling carousel of popular actions. Auto-advance slowly; pause on hover; swipeable on mobile.

TODO

• copy for the actions

Verification

bun run lint
bun run type-check
bun test

Visual QA: carousel auto-advances on load, pauses on hover, swipes on mobile (<768px).