Support loggers that uses process.stdout

[Lewenhaupt]

Something with the tsdown build is causing logging to completely break. I'm looking into it.

[Lewenhaupt]

After looking into the issue a bit more what seems to happen is that the node extension does correctly send, but the logs it outputs to the original console all become undefined.

[Lewenhaupt]

Ok I was using https://www.npmjs.com/package/pino-lambda which seems to be doing something odd, at least compared to standard pino. If I remove pino-lamda I get the logs in cloudwatch correctly via pino. I don't get the pino logs in Serverless-Spy though (because it doesn't use console, it uses process.stdout instead). So not an issue, but maybe something I want to implement support for.