[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.

首先，在 macOS 上复现 Copilot CLI 终端渲染器中的内容损坏，并比较 thinking/reasoning 和最终响应的流式传输。跟踪渲染器如何处理部分 token 和行更新；当流式输出与底层内容一致，且没有重复字符、截断或重复行时，即表示完成。

由索引模型根据 Issue 内容生成。