Background tasks · 3 + 4 + 7 combined

Data check

Checked against the installed Claude Agent SDK (0.3.280) type definitions and conduit's Claude translator. Task names below are the kind Claude really writes; I sampled them from this session's own background tasks.

Shown in the design	Where the SDK has it	Conduit today
Task count	Yes. `background_tasks_changed` sends the full live list on every change (and again on reconnect).	Dropped. Only "any tasks?" survives.
Task name	Yes. `description` on each task, e.g. "Run codex to implement ticket .1". Sentences, so they need truncating.	Dropped.
Kind (shell, subagent, workflow)	Yes. `task_type`.	Dropped.
Age ("6m")	Not directly. The list has no start time. Conduit can note the time it first sees each task. That's accurate, because conduit starts the Claude process and sees every task begin.	Not recorded.
Shell command	Indirect. Each task points at the tool call that started it, and that call holds the command.	In the transcript, not linked.
Stop one task	Yes. `stopTask(id)`.	Not wired. Stop interrupts the turn, which kills every task.

One catch with per-task stop. To use it, conduit declares a per-task stop control to the SDK. After that, the composer's main Stop only stops the current turn and leaves background agents running. That's arguably better, but it changes what Stop means, so it's your call. The pull-down below assumes per-task stop is on, plus "Stop all".

The combination

From 7: The tasks hang off the goal with a └ elbow, (The send badge from 7 was dropped in favour of 3's dots.)
From 3: The row is task chips, each with its kind icon and name. A phone shows the newest task as one chip, then "+N"; desktop fits four.
From 4: Tapping the row opens the pull-down: full names, the command or agent, the age, a stop button per task, and "Stop all".
No goal: The elbow goes away and the row sits right under the title, so the layout stays stable.

Composer indicator

Each of 3, 4 and 7 brought its own input-area signal. All three at once is too much, so pick one. Chosen: B, one dot per task. The combination above and the desktop mock use it.

Desktop

There's room for up to four chips with ages. On desktop the pull-down is a popover under the row instead of a full-width sheet. Tap the row to toggle it.