Sticky prompt textbox when scrolling chat history

Summary

Codex should support a sticky prompt textbox/composer: it stays in the normal chat-list flow when the user is at the bottom, but docks to the bottom of the screen when the user scrolls upward through history.

Problem

When reading older parts of a long conversation, the prompt textbox can end up far away from the user's viewport. That makes it awkward to inspect history and continue typing at the same time.

A better behavior would preserve both:

• proximity to the latest messages when the user is at the bottom
• constant input reachability when the user scrolls away from the bottom

Requested behavior

• when the user is at the bottom of the chat, keep the prompt textbox in the normal chat layout near the latest messages
• when the user scrolls upward, make the prompt textbox stick to the bottom of the viewport
• when the user returns to the bottom, let the prompt textbox rejoin the normal chat-list layout

Why this is useful

• keeps input reachable while inspecting earlier context
• avoids losing the composer during long-thread navigation
• preserves the feel that the composer belongs to the chat flow rather than always being detached

Success criteria

• scrolling upward keeps the prompt textbox visible at the bottom of the screen
• returning to the bottom restores the normal inline chat-flow placement
• the transition feels stable and does not introduce cursor/composer drift or layout jank

Related context

Closest adjacent issue:

• #11063

That ticket is about bottom-pane anchoring instability / jank. This request is the intentional UX feature: a sticky-on-scroll composer behavior.