agents-runtime: background compaction stays running after normal idle exit

**Versions**

Reproduced in a local TypeScript integration with agents-runtime 0.6.3 based on
`91758919586d7c0c70a7b8190a39b6e06fc2ea14`. This build has downstream compaction
configuration changes, but the background `processWake` lifecycle is unchanged.
I also inspected main at `bb397424db0e1c153dc356713fd3dfd40315470c`; the same
lifecycle is present there. I have not run the integration against that main SHA.

**Bug description**

Background compaction can finish successfully after the normal idle timeout
ends its wake, but its checkpoint stays `running` and the summary is never
applied. The original conversation remains available.

The non-blocking behavior in #4605 is intentional. The problem is the unfinished
checkpoint after the background work has ended, not that a user turn returns
before its summary finishes.

To reproduce without live inference, use a fixture turn whose reported usage
exceeds the background threshold and hold the public `summarizeComplete` hook
behind a barrier:

```ts
const gate = Promise.withResolvers()
const returned = Promise.withResolvers()
const summarizeComplete: NonNullable = async () => {
await gate.promise
returned.resolve()
return { content: [{ type: 'text', text: 'Generated summary.' }], stopReason: 'stop' }
}
```

1. Configure a 100 ms runtime idle timeout and a longer summary deadline.
2. Send one user message. Let the turn finish and background summarization start.
3. Keep the gate closed until the runtime reports that the wake has ended.
4. Resolve the gate and await `returned.promise`.
5. Read the persisted stream again. The latest status for that compaction
generation is still `running`; no `complete` or `failed` checkpoint is saved.

The local regression fails with `BACKGROUND_CHECKPOINT_MUST_FINISH`, after
confirming `summarySettled: true` and `checkpointStatuses: ["running"]`.
This uses controlled completion, not a sleep or a stopped runtime process.

In `packages/agents-runtime/src/process-wake.ts`, the promise callback only
updates the wake-local `pendingBackgroundCompaction` slot and interrupts an
active idle wait. After an idle timeout with a pending slot, the loop exits and
cleanup closes the writer and sends done. There is no continuation or
cancellation for that slot. A subsequent wake creates a new slot.

The 100 ms idle window makes the test quick. The defaults also allow this
ordering: 20 seconds idle versus a 120 second summary deadline. This does not
mean every background summary fails.

**Expected behavior**

On a normal idle exit, finish the generation through an owned continuation, or
cancel it and record a terminal status. Either policy is reasonable. A summary
that has finished should not leave an orphaned `running` checkpoint or perform
work whose result no active wake can use.