[FEATURE] Mods API: a queryable record per background task, with event order, exit code and progress

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

Downrange (github.com/dot-agi/downrange) is a mod that shows each background task's state, progress and ETA. It builds them from task notifications, Stop snapshots and output files.

Claude Code 2.1.296 (macOS) declares a task as:

type BackgroundTaskSummary = { id: string; type: string; status: string; description: string;
    command?: string; agent_type?: string; server?: string; tool?: string; name?: string; };

Gaps:

• No input carries an engine sequence or time. A late Monitor event can revive a finished row.
• $.agent.list() is the only on-demand list. Shells, Monitors and workflows have none.
• PromptOrigin { kind: 'task-notification' } has no task id. No typed field holds an exit code, so a missed notification leaves a shell row without one.
• No progress field. The mod parses ratios from output, so 10/11 moves the bar.

Proposed Solution

1. $.task.list(): Promise<TaskInfo[]> and $.task.get(id): Promise<TaskInfo | undefined> for all task types. Keep ended tasks briefly.
2. TaskInfo = BackgroundTaskSummary & { seq: number; updatedAt: number; exitCode?: number; endedAt?: number; progress?: { done: number; total?: number; label?: string } }. seq rises per session with each lifecycle change.
3. Add the task id and seq to the task-notification origin and to each Stop and SubagentStop background_tasks entry.
4. Fill progress only from a source the producer opts into, such as OSC 9;4 or a Monitor event field. Never from free text.

Alternative Solutions

#100201 asks for a hook event when a task ends. It fixes missed ends, but not order, exit codes or progress.

Priority

Medium - Would be very helpful

Feature Category

Developer tools/SDK

Use Case Example

This closes two Downrange known limits: "Inputs that reach Downrange late" and "Progress read from output". With seq, the mod drops stale inputs exactly.

Additional Context

Related: #95742 (notifications re-fire after a task is gone), #98816 (background_tasks includes ambient tasks), #87186 and #33310 (closed, narrower).