Alternate Buffer SettingsDialog

[psinha40898]

What would you like to be added?

Alternate buffer mode should render a version of the SettingsDialog that supports the new Scrolling components as well as mouse support.

Why is this needed?

It is a natural extension of the alternate buffer capabilities.

Additional context

The current SettingsDialog has excessive and redundant React State as well as Effect. The current implementation of the SettingsContext mandates that views reactive to Settings changes use React anti patterns.
It makes sense that all of this should be cleaned up before landing a conditionally rendered alternate buffer SettingsDialog for a few reasons:

1. The Alternate Buffer version should not ship with the React Anti Pattern
2. It will be easier to review
3. The non Alternate Buffer version of the SettingsDialog should be easy to maintain too

A full path toward refactor is outlined in #14915
The refactor path is related to #18980
The refactor path is related to #19093
The alternate buffer settings dialog is related to #10673
The alternate buffer settings dialog is related to #18441 and #17998 but maybe those can reasonably be hot fixed without regard for this refactor path

Just referencing the issues for clarity and context

[psinha40898]

/assign

[gemini-cli]

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[gemini-cli]

This is a medium-priority feature request to enhance the SettingsDialog with alternate buffer and scrolling support, also noting internal refactoring needs.