Fix extension startup initialization race

## Problem

`TestStartAndWaitExtension_PropagatesTraceContext` can time out instead of returning the extension process error. The extension startup goroutine and readiness waiter can concurrently call `Extension.ensureInit()`, causing the extension state—including `readySignal`—to be initialized more than once. The process error may then be delivered to a different channel from the one observed by `WaitUntilReady`.

This surfaced twice in the Windows build for #9934 and reproduces with the Go race detector. The defect already exists on `main`; it is not caused by the gRPC dependency update.

## Proposed fix

Initialize the extension standard streams/readiness state before starting the extension goroutine. This ensures both process failure signaling and readiness waiting use the same initialized state.

## Validation

Run the targeted test repeatedly with the race detector:

```sh
go test -race ./cmd/middleware -run "^TestStartAndWaitExtension_PropagatesTraceContext$" -count=100
```