follow-up: investigate alternate forms of error handling for web context

After 0xMiden/miden-client#813 the `set_once()` call was removed as it no longer worked. The problem it fixed was that rust panics hanged the web client tests instead of instantly failing.

We should look into new ways of dealing with rust panics in wasm context. @igamigo proposed [`unwrap_throw`](https://rustwasm.github.io/wasm-bindgen/api/wasm_bindgen/trait.UnwrapThrowExt.html) which might fix the issue by converting the panic into a js error which can be then handled.

Also, we can investigate if there are better ways of printing the js errors once they get catched in Rust (look in https://github.com/0xPolygonMiden/miden-client/pull/813#discussion_r2017639259 for context).

Untersuche das wasm-bindgen UnwrapThrowExt-Trait, um Rust-Panics in JS-Fehler umzuwandeln. Sieh dir die verlinkte PR #813-Diskussion für den Kontext zur Fehlerausgabe an. Beginne damit, den Setup der Web-Client-Tests und das aktuelle Verhalten von Panics zu verstehen. Ermittle, wie unwrap_throw integriert und die Fehlerbehandlung im Web-Kontext verbessert werden kann.

Vom Indexierungsmodell aus dem Issue-Text verfasst.