Let agents set a custom status icon for a session

Once you're running several sessions at once, the sidebar gets hard to keep track of. Every session shows a status indicator that reflects what's happening: animated while the agent is working, one color when it's done, another when it needs your attention. But when a session is idle, there's no icon at all, so a stack of idle sessions all look the same and it's tough to get a quick overview.

I'd like agents to be able to give a session its own custom icon. The agent picks a small symbol that represents what the session is about, and that icon shows up next to the session in the sidebar when it's otherwise idle. Think of it like the session's title, but visual: the agent decides on it as part of describing its work.

This feels especially worthwhile now that LLMs are getting genuinely good at producing SVG graphics. A model can draw a clean, recognizable little glyph for a task on its own, so the icon can actually reflect the content of the session rather than being picked from a fixed set.

**Why this is useful**
- Makes a screen full of sessions much easier to scan and tell apart.
- Gives idle sessions some identity instead of a blank slot.
- Lets the agent communicate the nature of a task visually, not just in text.

**Expected behavior**
- An agent can set a custom icon for its session.
- The icon appears in the sidebar when the session is idle.
- The existing working/done/needs-attention indicators still take priority when they apply, so this only fills the idle gap.
- The icon should stick around after a reload.
- This should work for both regular workspace sessions and general chat sessions.

Empieza rastreando el indicador de estado de la barra lateral para las sesiones inactivas y cómo se conserva el estado de la sesión tras recargar. Comprueba tanto las sesiones normales del workspace como las sesiones de chat general y, después, verifica que los iconos personalizados solo aparezcan cuando la sesión está inactiva, que los indicadores de estado existentes tengan prioridad y que el icono persista.

Escrito por el modelo de indexación a partir del texto del issue.