[BUG]: Terminal streaming renderer corrupts output - characters doubled/truncated during streaming

## Description

The Copilot CLI terminal renderer corrupts streamed output, producing doubled characters, truncated tokens, and repeated lines. This affects both the thinking/reasoning phase output and the final assistant response output.

## Steps to Reproduce

1. Ask Copilot CLI any question that produces a moderately long response
2. Observe the output as it streams to the terminal

## Observed Behavior

Output is visibly corrupted during streaming. Examples seen:
- Partial tokens rendered before full token is available (e.g. `apil` instead of `apiVersion`)
- Characters doubled mid-word (e.g. `obserrvability`, `permpermissions`)
- Words repeated mid-sentence (e.g. `New ReliNew Relic`, `useruser`)
- Lines repeated (e.g. `metadata:` block appearing twice)
- Thinking/reasoning tokens streamed visibly with same corruption artifacts

Example corrupted output observed:
```
apil
apiVersion: rbac.authorization.k8s.io/v1
...
- apiGroups: [piGroups: [""]
```

## Expected Behavior

Output should render cleanly with no corruption, doubled characters, or repeated lines.

## Environment

- Copilot CLI version: 1.0.61
- OS: Darwin (macOS)

## Notes

The underlying content being generated is correct — the issue is purely in how the CLI streams and renders tokens to the terminal.

Beginne damit, die Beschädigung im Copilot CLI-Terminal-Renderer unter macOS zu reproduzieren, und vergleiche dabei das Streaming von Thinking/Reasoning und der finalen Antwort. Verfolge, wie der Renderer partielle Tokens und Zeilenaktualisierungen verarbeitet; abgeschlossen ist die Aufgabe, wenn die gestreamte Ausgabe dem zugrunde liegenden Inhalt entspricht, ohne doppelte Zeichen, Abschneidungen oder wiederholte Zeilen.

Vom Indexierungsmodell aus dem Issue-Text verfasst.