See https://metacpan.org/pod/Log::Log4perl#Appenders and Log::Log4perl::Appender as Log::Log4perl::Appender::String docs have a mistake, you're supposed to write

Log::Log4perl::Appender->new(
    'Log::Log4perl::Appender::String', 
    "name" => 'string_appender',
);
[download]

This isn't the first time I've tripped over that :)