Improve autocomplete behaviour

[aibrahim-]

Task/Issue URL: https://app.asana.com/1/137249556945/project/1214157224317277/task/1214964760144656?focus=true

Description

Three related fixes around the native-input widget's autocomplete:

1. Avoid spurious "loading from scratch" on widget re-open with same text. showNativeInput dropped the onClearAutocomplete call that emptied searchResults and re-triggered a fetch; restores the suggestions list visibility from the adapter when the cache matches the prefill.

2. Reveal the browser behind the closing widget earlier. hideNtp now runs at the start of hideNativeInput so the webpage is visible during the exit animation, instead of after the 200ms exit + 150ms fade leaves the NTP background filling the screen.

3. Always keep an autocomplete cache for the omnibar's text so in-widget typing never permanently displaces the omnibar's results. Adds an always-on parallel pipeline in BrowserTabViewModel (omnibarAutocompleteCache) fed by onOmnibarTextChanged; the widget restores from it on close (non-navigation) and on open if the cache matches the prefill.

Steps to test this PR

• enable native input widget
• start a search by typing on the keyboard
• observe autocomplete
• going back should immediately display the web page.
• lauching the keyboard again should immediately display the autocomplete list.

UI changes

Before	After

---

Note

Medium Risk
Touches autocomplete flow logic and native-input widget lifecycle/teardown, which could cause regressions in suggestions rendering or keyboard/tab-switch behavior if the new caching and backgrounding hooks misfire.

Overview
Improves native-input widget autocomplete so reopening the widget with the same text can immediately reuse cached omnibar suggestions instead of clearing state and refetching.

Adds an always-on (setting-gated) omnibar autocomplete cache in BrowserTabViewModel, feeds it from rendered omnibar text, and exposes a restore path used when the widget opens/closes to prevent in-widget typing from permanently displacing omnibar results.

Tightens widget lifecycle behavior: reveals the live page earlier during exit (moves hideNtp), adds onTabBackgrounded to synchronously dismiss IME/tear down the widget on tab hide/swipe, guards enter-complete focus against detached views, and updates enter-animation preview to apply correct per-tab state for top/bottom layouts. Tests cover cache gating, restore behavior, and pixel implications.

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