fix: resolve grid line layout and studio project page state bugs

## Root Cause I investigated the codebase and found three distinct issues across two different files: 1. **CSS Selector Bug in `apps/learn/app/(app)/page.tsx`**: In the `Home` component, the code renders 13 vertical grid lines in a loop and attempts to hide the first and last lines using Tailwind's `first:hidden last:hidden` classes. However, the parent container also contains the "Grid Content" `div` as a sibling immediately after the mapped grid lines. Because this content `div` is the actual last child of the parent container, the CSS `:last-child` selector (which Tailwind's `last:` compiles to) targets the content `div` instead of the 13th grid line. This leaves the 13th grid line visible. 2. **Stale Input Value in `apps/lite-studio/app/routes/projects.$ref.tsx`**: In the `ProjectPage` component, the project name input field uses `defaultValue={ref}`. In React, `defaultValue` only sets the input's value on the initial mount. If a user switches projects (which changes the `ref` route parameter), the input field will not update to show the new project name because React does not re-mount the component. 3. **Uncleared Timeout in `apps/lite-studio/app/routes/projects.$ref.tsx`**: Also in the `ProjectPage` component, the "Refresh Status" button's `onClick` handler triggers a 2-second timeout to toggle the `loading` state back to `false`. This timer is never cleared. If the user navigates away or unmounts the component before the 2 seconds are up, React will attempt to update the state of an unmounted component, which triggers a memory leak warning. ## Evidence * **`apps/learn/app/(app)/page.tsx`**: I confirmed this by reading the `Home` component directly. The vertical grid lines are mapped inside a `relative` container, followed immediately by the "Grid Content" `div`. This structure breaks the `:last-child` CSS assumption. * **`apps/lite-studio/app/routes/projects.$ref.tsx`**: I confirmed this by reading the `ProjectPage` component directly. The `onC…