Sidebar: sort threads by when the agent last finished a turn

[grahamfarrar]

Problem

I run several agents in parallel, across a dozen projects, and the question I'm always asking the sidebar is "what just finished?" Today the only activity sort is "Last user message" (sidebarThreadSortOrder: updated_at), so a thread moves up when I send to it, not when the agent comes back. A thread I kicked off an hour ago that finished a minute ago sits below everything I've typed into since.

The status dot tells me a thread is done, but I still have to scan the whole list to find it.

Proposal

Add a third thread sort option, "Last agent reply" (or "Last turn finished"), keyed on the time the thread's most recent turn completed.

It moves a thread once per turn, at completion. It does not re-sort on every streamed message, which was the problem with a plain "last activity" sort in #6964 (threads bouncing while the agent writes). A thread that is still running stays where it is until its turn ends.

Ideally the same option on mobile, which #14196 asks for there.

Why not existing features

• "Last user message" orders by my input, not the agent's output.
• The Settled section and unread markers show state, but don't put the newest finished thread at the top of its project.
• Pinning is manual.

Related: #6964, #14196, #22288.