Style: Design System use across more components (#6705)

## Summary

Only remaining use is in `buttonTypes.ts` which @viva-jinyi is going to
be working on to consolidate our different buttons soon.

## Changes

- **What**: Replace light/dark colors with theme aware design system
tokens.

## Review Focus

Double check the chosen colors for the components

## Screenshots

| Before | After |
| ------ | ----- |
| <img width="607" height="432" alt="image"
src="https://github.com/user-attachments/assets/6c0ee6d6-819f-40b1-b775-f8b25dd18104"
/> | <img width="646" height="488" alt="image"
src="https://github.com/user-attachments/assets/9c8532de-8ac6-4b48-9021-3fd0b3e0bc63"
/> |

┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-6705-Style-WIP-Design-System-use-across-more-components-2ab6d73d365081619115fc5f87a46341)
by [Unito](https://www.unito.io)

---------

Co-authored-by: github-actions <github-actions@github.com>

src/components/widget/panel/LeftSidePanel.vue

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

src/components/widget/panel/RightSidePanel.vue

@@ -1,5 +1,5 @@
 <template>
-  <div class="h-full w-full bg-white pr-6 pb-8 pl-4 dark-theme:bg-charcoal-600">
+  <div class="size-full bg-modal-panel-background pr-6 pb-8 pl-4">
     <slot></slot>
   </div>
 </template>