Task/Issue URL:
https://app.asana.com/1/137249556945/project/1207418217763355/task/1215242220281929?focus=true

### Description

Adds Fire mode theme overlays for Duck.ai screens and widgets.

Figma link:
https://www.figma.com/design/9S33EK9qIxZdN1FOIFHM5W/%F0%9F%94%A5-Fire-Mode-Tabs--iOS-Android-?node-id=1846-13998&m=dev

### Steps to test this PR

- [ ] Enable the Fire tabs FF in dev settings
- [ ] Make sure Search & Duck.ai option is selected in AI settings
- [ ] Make sure the Light mode is set on a test device
- [ ] In the Tab switcher, switch to Fire mode
- [ ] Go back to the browser
- [ ] Verify that the browser is using the light mode but the native
input widget is using dark mode colors
- [ ] Verify the action buttons are using the Fire mode orange colors
- [ ] Switch to dark mode on the device
- [ ] Verify the dark mode theme is used everywhere


<!-- CURSOR_SUMMARY -->
---

> [!NOTE]
> **Low Risk**
> Theming and layout attribute changes across browser and Duck.ai UI
with no auth or data logic; regression risk is visual (Fire vs normal
themes, light Fire card contrast).
> 
> **Overview**
> Introduces **`daxInputModeCardThemeOverlay`** so Duck.ai / native
input **cards** can pick up Fire styling independently of the rest of
the screen. In **light Fire mode**, light Fire sets
**`ThemeOverlay.DuckDuckGo.InputModeCard.DarkFire`** on the card while
the activity stays on the light Fire theme—matching the Figma split
(light browser chrome, dark input card, orange accents).
> 
> Fire accents are centralized on new **`daxColorFireModeAccent*`** and
**`daxColorOmnibarAccentContent`** theme attrs; Fire themes and omnibar
overlays now reference those instead of hard-coded mandarin colors.
Input cards and send/outline controls switch from blue primary button
colors to **`daxColorOmnibarAccent`** /
**`daxColorOmnibarAccentContent`**.
> 
> **`InputScreenActivity`** applies the Fire theme when
**`BrowserMode.FIRE`**; bottom-bar **`InputScreenButtons`** are inflated
with the card’s themed context via new
**`InputModeWidget.cardContext`**. Omnibar tracker animations and
privacy shield rendering force the dark variant in Fire mode; the tab
switcher icon uses **`?attr/daxIconTabSwitcher`**.
> 
> <sup>Reviewed by [Cursor Bugbot](https://cursor.com/bugbot) for commit
9465d5bd2775956df65bceb036dbbd5943159e75. Bugbot is set up for automated
code reviews on this repo. Configure
[here](https://www.cursor.com/dashboard/bugbot).</sup>
<!-- /CURSOR_SUMMARY -->