[Feature] Interactive page indicator with sliding scrubbing and resting search shortcut (realme UI style)

Describe the feature

Add an interactive home screen page indicator that allows sliding over the dots to scrub between pages, transitioning into a small search button when resting to trigger the launcher search overlay.

Why would it be useful to add?

This provides a fluid navigation gesture while offering an extra, space-saving entry point for search that complements the existing dock search widget, especially useful when the dock is hidden or covered.

Did the feature exist in Lawnchair Legacy?

No

Example(s)

Behaves similarly to realme UI's launcher page indicator, where dragging the indicator scrolls the pages, and settling on the indicator displays a quick search trigger.

On Rest

On Dragging

On Dragging (2)

Additional context

Tested against the latest Lawnchair nightly builds; no existing equivalent behavior found in current indicator options. Avoid dragging on just holding the indicator bar to avoid accidental swap.