Custom async error handler

Implement support for a custom error log handler, so that asynchronous errors can be caught instead of (as now) be console logged.

Analyze whether this should be per-request, per-context and/or generic.

No files, tests, or entry points are named. Start by locating the asynchronous error path that currently logs to the console, then evaluate whether a custom handler belongs per request, per context, or generically; done means asynchronous errors can be caught through the chosen handler without console logging.

Written by the indexing model from the issue text.