[FEATURE] Mods: let a desktop pane dock below the conversation, on the left, or in its own tab, and honour columns

What would you like?

Let a mod's pane open somewhere other than the right-side dock on the desktop app, and let the person move it there:

• Placement: below the conversation (full width), on the left, or in its own tab or window, chosen by the person (drag the pane, or a menu on its tab), with the plugin able to state a preferred placement at $.ui.open (a hint, like columns and rows are today).
• Width: on desktop, honour columns the way the terminal's fullscreen dock does, so a pane whose content is a wide table opens wide enough to read without dragging.
• Remembered: the placement the person chose sticks for that pane id across sessions, as a dragged width already does.

Why

Mods are already useful as live views beside the conversation: a "what is this machine doing" pane (push queue, compute usage, local model server, containers), a checklist of steps the person must do. Some of that content is naturally wide: tables with a label column, an age column and a status, or log lines. In a right-side dock it wraps or truncates, and the conversation loses width while it is open. A full-width pane below the conversation (or a separate tab for something you glance at occasionally) would suit those views better, while short lists stay best on the side.

What the API offers today (2.1.286)

PaneOpenArgs takes rows (inline above the prompt) and columns (docked beside a fullscreen transcript); the surface decides the placement. There is no way for a plugin or the person to put a pane anywhere but those two places.

Related: #99449 (fixed, independently scrolling regions inside a desktop pane), #91870.

_Disclosure: this request was written with AI assistance (Claude Code), from our own use of mods; I have read it and stand behind the ask._