[refactor] Manager dialog design improvements (#8247)

## Summary
Refactored Manager dialog components for cleaner button rendering logic
and improved visibility.

## Changes
- **InfoPanelHeader**: Centralized button rendering logic (try update,
uninstall, install) instead of using slot overrides
- **PackTryUpdateButton**: Changed variant from `textonly` to `inverted`
for better visibility
- **InfoPanel**: Removed slot override and unused imports, simplified
component
- **ManagerDialog**: Design modifications for improved UX
- **PackCard/PackBanner**: Component refinements
- **useManagerDisplayPacks**: New composable for display pack management

## Review Focus
- Button visibility and styling with `inverted` variant
- Centralized button logic in InfoPanelHeader

## Before

[manager-before.webm](https://github.com/user-attachments/assets/4cef5f10-9cb2-4a31-a095-b170643e481d)

## After

[manager-after.webm](https://github.com/user-attachments/assets/9b693b32-59ca-4c88-b7e7-9a78aba19df7)

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-8247-refactor-Manager-dialog-design-improvements-2f06d73d365081bf9f07efa043caa378)
by [Unito](https://www.unito.io)

src/components/widget/nav/NavItem.vue

@@ -3,7 +3,7 @@
     v-tooltip.right="{
       value: tooltipText,
       disabled: !isOverflowing,
-      pt: { text: { class: 'whitespace-nowrap' } }
+      pt: { text: { class: 'w-max whitespace-nowrap' } }
     }"
     class="flex cursor-pointer select-none items-center-safe gap-2 rounded-md px-4 py-3 text-sm transition-colors text-base-foreground"
     :class="