AdminEmailHandler and BrokenLinkEmailsMiddleware raise on email transport errors when MAILERS is configured

[Adam Johnson]

Since #35514, Django’s built-in error reporting emails (admin emails and broken-link emails) raise on any transport error when the new dictionary-based MAILERS setting is configured, instead of failing silently as they did in Django 6.0.

Specifically:

• AdminEmailHandler.emit() has no surrounding try/except, and Python's logging machinery does not contain exceptions raised by emit(), so the transport error is raised at the logger.error(...)/logger.exception(...) call site — i.e. inside Django's own error-handling path while reporting a 500.

• BrokenLinkEmailsMiddleware.process_response() raises on every referred 404, turning it into a 500.

The new "Migrating email to mailers" howto recommends wrapping sends in an error handler with try: / except Exception: pass "to avoid cascading failures inan error handler that sends mail".
We need to apply that advice to Django's own built-in error handlers!