Project filter: show which projects have threads that need attention

[liaugust]

Problem

I usually filter the sidebar to one project at a time. While the filter is on, I can't see the other projects. A thread elsewhere can finish, fail, or start waiting for my input, and I won't know until I clear the filter or switch to that project. The project filter popup is where I pick the next project, but it doesn't say which project needs me.

Proposal

In the existing project filter popup, show a small status indicator next to each project when any of its threads is in a state worth noticing:

• Working: a turn is running
• Waiting on me: an approval or input request is pending
• Failed: the last turn errored
• Completed, unseen: a turn finished and I haven't opened the thread

Rules:

• Roll threads up to one indicator per project and show the highest-priority state: failed > waiting on me > completed unseen > working.
• Skip settled, snoozed, archived, and subagent threads, matching the sidebar's existing status logic.
• Reuse the status dots and colors the sidebar thread rows already use, and add a tooltip or accessible label (for example "2 waiting, 1 running") so the indicator doesn't rely on color alone.
• Optionally, show the same indicator on the filter button itself when a project hidden by the filter needs attention.

The change is limited to the current popup. It adds no new sidebar layout and no new setting.

Prior art

• feat(web): show attention status dots in the project switcher #7954 proposed attention dots in the project switcher and was closed with a request for an Ideas discussion. That's what this is.
• feat(web): show project attention in switcher #7955 already has an implementation, but was closed because it lacked prior approval of the direction.
• Sidebar: always-visible project icon row as a one-click filter #22959 proposes an always-visible project icon row with activity dots. This proposal is the smaller version that keeps the current picker.
• Always-visible thread tally per project (in-app strip + tray) #21703 proposes a per-project thread tally strip and tray icon. It's related but broader.

If this direction is approved, I'm happy to open a PR, building on #7955 where it makes sense.