Investigate returning `js_sys::Error` on the web client

As of https://github.com/0xPolygonMiden/miden-client/pull/786, we added more context to the error messages returned as `JsValue`s by concatenating source errors together. @dagarcia7 suggested looking into returning `js_sys::Error` as a future improvement, adding more context by returning Javascript-native errors.

Reference: https://github.com/0xPolygonMiden/miden-client/pull/786#pullrequestreview-2696966230

Look at the error handling in the web client, likely in the WASM bindings where JsValue is returned. Review PR #786 to understand the current concatenation approach. Investigate js_sys::Error API to see how to convert existing errors into native JavaScript errors. Test changes in a browser environment to ensure errors are properly thrown and catchable.

Written by the indexing model from the issue text.