fix(tasks): address task API review feedback

The public kill result used the awkward phrase already-terminal. Rename it to already-finished and keep the model-facing response aligned; not-alive would be inaccurate because a force-failed registry record can still correspond to orphaned producer work.

Task kinds were open strings even though producer namespaces are an extension point. Add the merge-extensible TaskKindMap and derived TaskKind, cover consumer declarations in task and bundle tests, and retain the runtime non-empty check for untyped callers.

With exactOptionalPropertyTypes, owner?: Agent | undefined allowed an explicit undefined value that no caller needs. Tighten the property to owner?: Agent so unowned work is expressed by omitting it.

Record the requested task-service/backend split as a follow-up, using a systemd-backed runtime as a concrete candidate without guessing its durability and ownership contract in this PR. Regenerate the type and Cordis catalogs so public docs match the declarations.

docs/core-data-structures/tasks.md

@@ -4,7 +4,16 @@ Types shared by long-running producers, `ctx.tasks`, and task control surfaces.
 
 ## Ids and status
 
-`TaskId` is a [branded id](core.md#branded-ids) generated as `<kind>-N`. Access control relies on owner authorization, not id secrecy. `TaskStatus` is `'running' | 'stopping' | 'completed' | 'killed' | 'failed'`; producer-specific facts belong in `TaskSnapshot.detail`.
+`TaskId` is a [branded id](core.md#branded-ids) generated as `<kind>-N`. Access control relies on owner authorization, not id secrecy. `TaskKind` derives from a merge-extensible map; the registry treats kinds as opaque id namespaces.
+
+```ts type-equiv
+interface TaskKindMap {
+  bash: 'bash'
+  subagent: 'subagent'
+}
+```
+
+`TaskStatus` is `'running' | 'stopping' | 'completed' | 'killed' | 'failed'`; producer-specific facts belong in `TaskSnapshot.detail`.
 
 ## Producer contract
 
@@ -12,17 +21,17 @@ Types shared by long-running producers, `ctx.tasks`, and task control surfaces.
 
 ```ts type-equiv
 interface TaskStart {
-  /** Producer kind — also the id prefix (`bash`, `subagent`, …). Non-empty. */
-  kind: string
+  /** Producer kind — also the id prefix (`bash`, `subagent`, …). */
+  kind: TaskKind
   /** One-line model-facing label (the command; the delegation description). */
   label: string
   /**
    * Owning live agent. Access is fenced by its session id, and agent disposal
    * cancels and awaits the task. The instance must be the one currently
-   * registered under its agent id. `undefined` creates an unowned task, open to
-   * any caller until service disposal.
+   * registered under its agent id. Omitting the owner creates an unowned task,
+   * open to any caller until service disposal.
    */
-  owner?: Agent | undefined
+  owner?: Agent
   /**
    * Start the work after preflight and synchronously return its hooks. Called
    * once; a throw leaves nothing registered, and the producer must clean up any
@@ -77,7 +86,7 @@ interface TaskSnapshot {
   /** The registry-issued id (`<kind>-N`). */
   id: TaskId
   /** The producer kind the task was registered with. */
-  kind: string
+  kind: TaskKind
   /** The producer-supplied one-line label. */
   label: string
   /**