fix(hono): Align error mechanism

> [!NOTE]
> The pull request "[fix(hono): Align error mechanism](https://github.com/getsentry/sentry-javascript/pull/19831)" was created by @s1gr1d but did not reference an issue. Therefore this issue was created for better visibility in external tools like Linear.

Mentioned here: https://github.com/getsentry/sentry-javascript/pull/19817#discussion_r2945636644

