[codex] Add Agent companion desktop pet

[bobleer]

Summary

• persist Agent companion pet selection and display mode across restarts
• add desktop floating pet mode with a transparent Tauri window, 96px pet rendering, bottom-right positioning, and cross-platform window setup
• sync companion mood and multi-session task bubbles from active session state, with stable bubble ordering
• restore normal chat input controls when the companion is shown as the desktop pet

Why

Users reported that selected companion images reset after restarting BitFun, desktop pet mode needed to become the default companion display, and companion visuals stayed idle during active sessions. The desktop pet also needed task status bubbles for concurrent sessions.

Validation

• pnpm run type-check:web
• pnpm run lint:web
• pnpm --dir src/web-ui run test:run
• cargo check -p bitfun-desktop
• cargo test -p bitfun-desktop