[FEATURE] Desktop: distinguish "blocked on permission" from "finished, awaiting reply" in session attention dots

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

In the Desktop app's session list, the yellow "needs input" dot covers two very different situations, rendered identically:

1. Blocked mid-turn — a permission prompt is up and the agent is halted. Work is stopped; every minute it goes unnoticed is wasted wall-clock time. Urgent.
2. Turn complete, awaiting reply — the agent finished its response and ended with a question or a deliverable. Nothing is running; nothing is lost by replying later. Not urgent.

When running several sessions concurrently (4–8 is normal for me), triage happens entirely in the sidebar, and it depends on trusting the indicators. One overloaded yellow signal trains you to stop reacting to yellow — and then the one genuinely costly case, work silently halted on an approval, is exactly what gets missed.

Worth noting: the blue unread dot already has coherent semantics — it appears when there's something new and clears when you read it. It's great. This request is essentially "give the yellow state the same level of coherence."

Proposed Solution

Split the yellow state into two visually distinct indicators (color, shape, or badge):

• Blocked / needs action to resume — should persist and nag until the prompt is answered; that's its job.
• Finished / has a question or deliverable for you — could adopt read semantics like the blue dot, since once you've seen it, you know.

Related issues (complementary — I support these too)

This sits alongside some existing requests rather than duplicating them:

• #51831 — read-state not clearing on viewed sessions (bug)
• #59740 — manual dismiss/acknowledge for the "Needs input" state
• #67533 — marking a conversation completed doesn't clear "Needs input"

All three would improve things and I'd love to see them land. This request is orthogonal: even with all of them fixed, the two yellow situations above would still be indistinguishable at a glance, and they have very different urgency.

Environment

Claude Desktop 1.11847.5, macOS 26.5

🤖 Drafted with Claude Code