refactor: route quote page through apiClient

[gaoflow]

Summary

• route quote requests through the shared apiGet/apiClient path
• add success and API/network failure toast feedback while keeping inline status/alert regions
• extend quote tests for URL encoding, multi-hop success, ApiError bodies, network rejection, validation guards, and loading state

Closes #1

Tests

• npm test -- src/app/quote/page.test.tsx --runInBand
• npm run lint
• npm test -- --runInBand
• npm run build
• NEXT_PUBLIC_STABLEROUTE_API_BASE=http://localhost:3011 npm run build
• Rendered smoke: started a temporary mock quote API on 3011 and production Next server on 3010, then captured /quote with Playwright CLI.

Browser runtime fallback: the in-app Browser was available as a skill, but the runtime returned Browser is not available: iab; I used Playwright CLI screenshots instead.

Screenshot evidence saved locally:

• /tmp/stableroute-quote-apiclient-toast.png

[mikewheeleer]

thanks for jumping in @gaoflow! 🙏 we assign issues before work starts so two people don't build the same thing, and #1 isn't assigned to you. please grab an open unassigned issue and PR against that. closing this one for now, hope to see you back 💪