Docs title-bar width toggle: click sticks, icon never updates, and layout flashes on refresh

Bug: docs title-bar width toggle is broken

The expand/collapse button next to "Copy page" on docs pages (visible at ≥1535px viewport) has three issues:

1. Click works only once, then gets stuck. Starting collapsed, the first click expands the layout. Subsequent clicks do nothing. Same in reverse: starting expanded, the first click collapses but it can't be re-expanded.
2. Icon never updates. Even when the layout state changes (e.g., on first click), the icon stays as UnfoldHorizontal (arrows pointing outward). It never flips to FoldHorizontal.
3. Flash on every refresh. When the preference is set to "expanded", refreshing the page paints the constrained (narrow) layout first, then snaps to expanded after hydration.

Repro

1. Open any docs page at a viewport ≥1535px (e.g. https://tanstack.com/router/latest/docs/framework/react/overview)
2. Click the expand/collapse icon on the right of the title bar
3. Try clicking it again — nothing happens, and the icon hasn't changed
4. Refresh while in the expanded state — observe the brief narrow → expanded flash

Video

https://github.com/user-attachments/assets/5a9b6ad5-5ca9-48d6-ad61-7b3dfa990096

I have a working branch with this fix locally. Will open a PR shortly ...

打开提供的 URL 中复现的 docs 页面，检查“Copy page.”旁边标题栏中的展开/折叠控件。验证该切换控件可以反复改变状态，图标会反映每种状态，并且在刷新后，展开的偏好设置不会短暂显示受限布局。issue 中未指定源文件或测试路径。