[FEATURE] Mods: let a docked Pane span the full height, beside the prompt

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

In fullscreen mode, a plugin Pane opened with $.ui.open docks beside the transcript only. The prompt box always spans the full terminal width underneath both. So the dock's height depends on the prompt's: every line I type, and every time the prompt grows (a long draft, a pasted block, the permission dialog), Claude Code takes that row from the pane as well as from the transcript.

For a pane that is a fixed dashboard, that means it constantly shrinks and grows while I type.
My pane shows the context forecast and rate limits at the top and a small animated scene underneath, drawn with a Raster sized from scroll.bodyRows. That scene is re-laid-out on every prompt line. The content never needed to change size; only the layout forces it.

Proposed Solution

An opt-in on PaneOpenArgs for the docked placement, for example:

await $.ui.open({ id: 'token-weather', columns: 62, dock: 'full' })

With dock: 'full', the dock would span from the top of the screen to the bottom, beside the prompt too. The prompt box and its hint line would take the remaining width. Without it, nothing changes.

bodyRows would then stay constant while typing, changing only when the terminal itself is resized.

Alternative Solutions

• Sizing the pane's content to bodyRows and reflowing on each render works, but the pane visibly shrinks and grows with every prompt line.
• rows on ui.open only applies to the inline placement; the dock ignores it.
• Pinning content to the top of the pane and letting the bottom be clipped hides the movement but cuts off whatever is drawn at the bottom.

Priority

Low - Nice to have

Feature Category

Interactive mode (TUI)

Use Case Example

1. I keep a mod pane docked on the right, showing live context use, the 5h/7d limits and a small animated scene.
2. I start typing a multi-line prompt.
3. Today, the pane loses one row per prompt line and its contents shift up each time.
4. With a full-height dock, the pane would stay the same size, like a sidebar in an editor, while the prompt grows in the space to its left.

Additional Context

• Claude Code 2.1.296, Linux, kitty, "tui": "fullscreen", pane docked at 62 columns.
• PaneOpenArgs.columns already describes the dock as opening "floor to ceiling", which in practice means the transcript's floor, above the prompt.
• Screenshot:

<img width="2877" height="1730" alt="Image" src="https://github.com/user-attachments/assets/6e9a59eb-9215-461f-af4f-2d2bad711e09" />
<img width="2877" height="1733" alt="Image" src="https://github.com/user-attachments/assets/b5dc15a3-a783-403d-923b-b2c0ad0d9837" />