feat(vite-example): add resizable chat panels

[oliverlaz]

🎯 Goal

Implement the dynamic panel resizing ticket in the Vite example app as the first iteration before extracting the behavior into SDK components.
Reference: the dynamic panel resizing ticket covering the channel list, message list, and thread panel behavior.

Resolves: https://linear.app/stream/issue/REACT-828/layout-panel-resizing

🛠 Implementation details

• persist left and thread panel layout in the existing example state store
• split examples/vite/src/App.tsx layout concerns into focused ChatLayout modules for panel rendering, resize behavior, URL/state sync, and shared constants
• add desktop drag resizing for the left sidebar and thread panel, including collapse and restore behavior, width constraints, and sidebar state synchronization with navOpen
• keep the chat view selector stable on desktop and tune transition handling so drag remains responsive while automatic sidebar collapse still animates

🎨 UI Changes

Example app layout behavior update:

Screen.Recording.2026-03-14.at.19.29.01.mov

[github-actions]

Size Change: 0 B

Total Size: 435 kB

ℹ️ View Unchanged

Filename	Size
./dist/audioProcessing-BbOs2wMd.js	1.32 kB
./dist/Channel-BbSF8w4p.js	20.2 kB
./dist/ChannelPreview-C8OPJzUm.js	14.1 kB
./dist/cjs/emojis.js	2.97 kB
./dist/cjs/experimental.js	3.81 kB
./dist/cjs/index.js	217 kB
./dist/cjs/mp3-encoder.js	1.27 kB
./dist/css/index.css	44.3 kB
./dist/css/v2/emoji-mart.css	1.84 kB
./dist/css/v2/emoji-replacement.css	300 B
./dist/css/v2/index.css	39.4 kB
./dist/css/v2/index.layout.css	22.8 kB
./dist/limits-D8PvuaTc.js	65.3 kB

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