Task/Issue URL:
https://app.asana.com/1/137249556945/project/1207418217763355/task/1215275434974447?focus=true
### Description
This PR implements the functionality that allows launching NTPs
specifically in Regular or Browser mode.
### Steps to test this PR
- [ ] Enable Fire tabs FF in dev settings
- [ ] Make Search & Duck.ai option is enabled in AI settings
- [ ] Open a new Duck.ai chat tab in Regular mode
- [ ] Tap on the + button and tap on "New Fire tab"
- [ ] Verify a new tab is launched and the browser is now in Fire Mode
(Fire mode theme is used)
- [ ] While in Fire Mode, open Duck.ai chat tab
- [ ] Tap on the + button and tap on "New tab"
- [ ] Verify a new tab is launched and the browser is now in Regular
Mode (regular theme is used)
<!-- CURSOR_SUMMARY -->
---
> [!NOTE]
> **Medium Risk**
> Touches core BrowserActivity lifecycle, mode switching, and intent
handling; incorrect deferral or replay could drop tabs or mishandle
launch intents, though ProcessIntent consumption is explicitly guarded.
>
> **Overview**
> Adds **mode-aware new tab launches** from Duck.ai’s “+” menu: **New
tab** switches to Regular mode first; **New Fire tab** switches to Fire
mode first.
>
> Replaces the old FIRE→REGULAR-only deferred `Intent` stash with a
general **`switchModeThen`** flow: pending work is stored as
**`PendingModeSwitch`** (`ProcessIntent` or `OpenNewTab`), saved in
instance state across activity recreate, then replayed in
`showWebContent`. **`launchNewTab`** gains an optional **`browserMode`**
parameter (default: current mode) and always goes through that deferral
path when a switch is needed.
>
> New **`PendingModeSwitch.kt`** defines bundle round-tripping;
**`PendingModeSwitchTest`** covers encode/decode edge cases.
**`runAction`** documents that carried intents are consumed via
`processIntent`, not re-launched.
>
> <sup>Reviewed by [Cursor Bugbot](https://cursor.com/bugbot) for commit
407bc24427f1adfed325193d32ae894d324faa97. Bugbot is set up for automated
code reviews on this repo. Configure
[here](https://www.cursor.com/dashboard/bugbot).</sup>
<!-- /CURSOR_SUMMARY -->
---------
Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>