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>

tests-ui/CLAUDE.md

@@ -1,5 +1,11 @@
 # Unit Testing Guidelines
 
+## Running Tests
+- Single file: `pnpm test:unit -- <filename>`
+- All tests: `pnpm test:unit`
+- Wrong Examples:
+  - Still runs all tests: `pnpm test:unit <filename>`
+
 ## Testing Approach
 
 - Write tests for new features
@@ -11,3 +17,7 @@
 - Check @tests-ui/README.md for guidelines
 - Use existing test utilities
 - Mock external dependencies
+
+## Mocking
+- Read: https://vitest.dev/api/mock.html
+- Critical: Always prefer vitest mock functions over writing verbose manual mocks