Asset Browser Design Review + Filters (#5737)

## Summary

Fixed design feedback and wired up the filter controls.

## Review Focus

Design Feedback:
-
[4872888](48728881af)
-
[9a0b63e](9a0b63edce)

Filters Hookup:
-
[07f22f8](07f22f8074)

Misc (can focus less on):
- claude guidance:
[23e6fa9](23e6fa9723)
- test helpers:
[7801ed9](7801ed9e28)

## Screenshots (if applicable)
<img width="1534" height="1175" alt="Screenshot 2025-09-23 at 1 03
12 PM"
src="https://github.com/user-attachments/assets/d82088e4-7d72-4c6f-904e-5180774d64a5"
/>

<img width="1794" height="793" alt="Screenshot 2025-09-23 at 1 03 22 PM"
src="https://github.com/user-attachments/assets/56eac2ba-5ecc-4a20-843f-ce683dea668c"
/>

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-5737-Asset-Browser-Design-Review-Filters-2776d73d3650813e890bd16fa6a0433f)
by [Unito](https://www.unito.io)

---------

Co-authored-by: Alexander Brown <drjkl@comfy.org>
Co-authored-by: GitHub Action <action@github.com>

src/components/widget/panel/LeftSidePanel.vue

@@ -1,5 +1,5 @@
 <template>
-  <div class="flex flex-col h-full w-full bg-white dark-theme:bg-zinc-800">
+  <div class="flex flex-col h-full w-full bg-white dark-theme:bg-charcoal-600">
     <PanelHeader>
       <template #icon>
         <slot name="header-icon"></slot>