[FEATURE]: TUI plugin API: let plugins add a tab to the composer picker #59650

Feature hasn't been suggested before.

• I have verified this feature I'm about to request hasn't been suggested before.

Describe the enhancement you want to request

In the V2 TUI, the Down key opens the composer picker (session.child.first, "Toggle subagent picker"). The picker has three tabs: Subagents, Shells and Terminals. Left and Right move between the tabs.

A TUI plugin cannot add a tab to this picker:

• The composer adds its tabs through ComposerContext.register (packages/tui/src/routes/session/composer/index.tsx:47, composer/context.ts:8-18). This context is internal to the TUI.
• The same file sets the three tab components (composer/index.tsx:127-130).
• The TUI plugin API has no slot or registry for the picker. The slot map has session.composer.top and session.panel, but no slot in the picker (packages/plugin/src/tui/context.ts:191-202).

I checked these files at the v2.2.0 tag. They are the same in 2.1.4.

Request: let a TUI plugin add a tab to the composer picker.

Example: a plugin sends messages and notices to sessions, for example messages from other sessions, subagent results and scheduled reminders. The TUI shows each one as a one-line synthetic message. A plugin tab in the picker can list these items with their sender and type, and expand one item to show its full text. Users then find these items in the same area as subagents and shells.

Possible API (a suggestion only):

const remove = ctx.ui.composer.tab({
  id: "mail",
  label: "Mail",
  order: 40,
  hints: () => [{ label: "expand", shortcut: "enter" }],
  render: (input: { sessionID: string; active: boolean }) => <MailTab {...input} />,
})
// remove() takes the tab out of the picker

• The host keeps the picker layout, the Left and Right tab keys, and the focus.
• The plugin tab gets the Up, Down and Enter keys while it is the active tab, the same as the built-in tabs.
• The host removes the tab when the plugin stops.

This API uses the current ComposerTab fields (id, label, hints) and adds order and render.

Current workaround: the session.panel slot with ui.panel.open(name). It works, but it opens a different view with a different key. Users must then look in two areas for related items.

Related: #59432 (render synthetic messages with a plugin component), #51209 (expose the V2 TUI composer to plugins), #51903 (composer tabs are not clickable).