The problem is almost exactly the same as described ZBX-9654.

Scenario.
1. Configure jabber and email media types.
2. Configure jabber to a real XMPP server.
3. Configure plain email to 1.2.3.4 (to simulate server that is slow).
4. Disable database.

Expected: jabber message sent to indicate DB failure.

Actual: watchdog is stuck with sending email to 1.2.3.4.

What makes this particularly bad is that failed alert sending is not even logged.

Currently visible solutions:
1. Whatever is implemented in ZBX-9654 is ported for watchdog.
2. Pass the watchdog generated alerts somehow to the alerter.