Report handlers via error handler instead of console

[chvp]

We got some reports mentioning an alert cause by errors here. Instead of logging details in the console we should send them to sentry (which is handled on the Dodona side).

I checked for other uses of console.log or console.error. There were no occurrences except for in Logging.ts, but that is not actually sent any error events. It's hard to get the error handler there, so I just left it as is.

[Copilot]

Pull request overview

This PR improves error reporting by routing errors to Sentry instead of logging them to the console. The changes replace console logging with calls to an error handler that can be configured via setErrorHandler().

Key Changes

• Added error capturing in the previously empty catch block when launching the runner
• Replaced console.error with errorHandler call when service worker registration fails
• Both error handlers now create Error objects with cause chaining for better error context

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