Stop: the turn vs background tasks

The SDK catch

A options: Work today. Conduit's Stop closes the Claude process, which kills every task whatever else we declare. The pull-down's per-task stops still work.
B, C, D options: Need two changes. Conduit declares per-task stop to the SDK, and Stop goes back to interrupting the turn instead of closing the process. Then the SDK lets background work keep running when you stop the turn.

Unverified for shells. The SDK docs say an interrupt then spares "background agents and workflows". They don't mention background shell commands like pnpm dev. Before building any B, C or D option, a short test should confirm a background shell survives a turn-only stop.

My pick: B3. Stop ends only the turn, then a toast by the composer offers "Stop them" for a few seconds. You get your two-press flow without a double-tap killing your dev server, and the header pull-down covers everything after the toast fades. If you want exactly your idea, C2 is the safer form of it.

Compare

Option	■ means	Stop everything	Mis-press risk
A1 Today	Turn + all tasks	1 tap	High. Kills tasks you wanted.
A2 Says so	Turn + all tasks	1 tap	High, but warned.
B1 Header owns tasks	Turn only	3 taps, in the header	None.
B2 Dots are a button	Turn only	3 taps, by the composer	None.
B3 Toast offer	Turn only	2 taps	Low.
C1 Second press	Turn, then tasks	2 taps	High. Double-tap, and the button stays armed for hours.
C2 Second press, 4 s	Turn, then tasks	2 quick taps	Medium. Double-tap.
C3 Hold for all	Tap turn, hold all	1 hold	Low, but hidden.
C4 Hold for menu	Tap turn, hold menu	Hold + 1 tap	Low, but hidden.
D1 Split button	Turn; ⌄ opens menu	2 taps	Low.
D2 Stop asks	Asks if tasks run	2 taps	None, but slowest.
D3 Two buttons	■ turn, blue grid tasks	2 taps	Medium. Wrong button.

A · Stop keeps ending everything

No change to what Stop means. Per-task control lives only in the header pull-down.

B · Stop ends only the turn

Background work survives Stop. The options differ in where you go to stop it.

C · One button that escalates

Your idea and its variants: ■ stops the turn first, and the same control can then stop the tasks.

D · Ask, split, or two buttons

The choice is explicit in the composer itself.

Your call

Desktop add-on, works with any option: Esc stops the turn, and a second Esc within a second stops the tasks.