StructuredLogFormatter exceptions are not visible to the user #43384
Description
Currently, if StructuredLogFormatter throws an exception it is silently swallowed and the user doesn't know something has gone wrong. PR #43371 provides one possible fix where we print the exception directly, however, we might be better trying to hook into the support of the underlying logging framework.
Logback has the concept of a Status event which it uses to pass exceptions raised from a LogEncoder. It also has a OnErrorConsoleStatusListener which will print errors to System.err.
Log4J2 has a DefaultErrorHandler which either ignores exceptions or throws a AppenderLoggingException.