Activity badge shows "7 running tasks" across all clients while backend task registry is empty; no way to clear over Remote Control

Environment

• Claude Code CLI on Linux (Debian 13), session driven via Remote Control from Claude Desktop (Windows) and claude.ai/code
• CLI version: 2.1.172 (Claude Code)
• Model: Fable 5

What happened

During a long session the model started ~10 background tasks (Bash run_in_background + Monitor watch loops for CI runs). Several of them delivered their completion/timeout notifications while the user had interrupted the turn (multiple user interruptions during the session).

End state — the activity line shows "✦ 7 running tasks", and crucially it shows the same count in both Windows Desktop and claude.ai/code, so the counter appears to be server-side session state rather than a local rendering issue.

Every backend probe disagrees with the badge:

• TaskStop returns "No task found" for all finished task IDs (registry already reaped them)
• TaskList is empty
• the host's process table shows exactly one live monitor process (the only genuinely running task)

So the badge seems to increment on task start but miss decrements when completion events land during interrupted turns — about 7 of 10 completions in this session coincided with interruptions, matching the displayed count.

Compounding issue

/tasks responds "/tasks isn't available over Remote Control." — so a Remote Control user has no way to inspect or dismiss the ghost entries at all.

Expected

• The running-tasks badge reconciles with the actual task registry (or decrements reliably even when the completion event arrives during an interrupted turn), and/or
• /tasks is available over Remote Control so stale entries can be inspected/cleared.

(Report drafted by Claude Code from inside the affected session, at the user's request — happy to provide task IDs/timestamps if useful.)