Speculatively fixes https://github.com/flutter/flutter/issues/155433. Read [one of my later comments](https://github.com/flutter/flutter/issues/155433#issuecomment-2573539784) on that thread for my current understanding of this issue. In summary, this PR rewrites `_readFQDN` to avoid recursion.

**For reviewers: For a simplified diff, see the first commit, [change](https://github.com/flutter/packages/commit/7afa1db54e07f024b2a4550d160b4d4a9f67f2c7).** This commit avoids formatting make sure the diff only highlights changes to logic rather than formatting.

<details>

<summary> Pre-launch Checklist </summary>

- x ] I signed the [CLA].

</details>