feat(tools): live dispatch lifecycle + native-contract parallel sub-calls in Code Mode

The bridge replaces its serialization queue with a pool that reuses the
native concurrency contract: submissions classify through
registry.executionMode (fail-closed isConcurrencySafe), start strictly in
submission order, overlap up to the validated maxParallelSubCalls config
(default 10; 1 restores serial), and exclusive calls drain the pool, run
alone, and bar later calls. Each started sub-call logs a
tool/code-dispatch-start event at pool entry; the existing
tool/code-dispatch settles the pair (started ⇔ settles exactly once;
abandoned queued calls log neither). SDK prompt guidance now states the
true Promise.all contract — re-recorded across every code/both-mode
snapshot (plus the stale cordis-dynamic-toolchain fixture gaining the
required description arg).

Client: CodeSubCall widens to RunningToolCall | ToolResultNode — starts
land the running shape (rows wear the native running ring), settles
replace in place preserving start order, callTime pairs to the start
time. Fixture emits start/settle pairs; jsdom pins the running sub-row;
runtime specs pin in-place settlement and out-of-order completion.

packages/client/ui-conversation/tests/chat-code-subcalls.spec.tsx

@@ -199,6 +199,21 @@ describe('run_code sub-calls through the real chat machinery', () => {
     expect(nest!.querySelector('[data-sample="bash-global"]')).not.toBeNull()
   })
 
+  it('a started-but-unsettled sub-call renders the running state exactly like a native in-flight row', async () => {
+    const parent = 'call-live'
+    const runningSub: CodeSubCall = {
+      callId: `${parent}:code:1`, name: 'grep', argsRaw: '{"pattern":"todo"}',
+      turn: 0, step: 0, time: 21_000, callView: null,
+    }
+    const dispatches = new Map([[parent, [runningSub]]])
+    const b = await bench(snapshotWith([], dispatches, [runningCode(parent)]))
+    const view = mountApp(b.slots)
+    // The nested row derives 'running' from the RunningToolCall shape — the
+    // same StateDot ring a native in-flight row wears.
+    const nested = view.container.querySelector('[data-subcalls] [data-variant][data-state="running"]')
+    expect(nested).not.toBeNull()
+  })
+
   it('an ordinary tool row renders no sub-call nest', async () => {
     const parent = 'call-64'
     const plain: ToolResultNode = {