GAE node.js console.error() not logging as ERROR log level

tl;dr - it's not supported.

Longer Answer

So it seems like Google has updated their documentation since I've posted my question. They've clarified that writing to stdout and stderr is collected, but:

does not provide log levels that you can use for filtering in the Logs Viewer

It's great that I have an answer, which is: "No, console.log() and console.error() will not have log levels." This kind of contradicts the next paragraph. I may be misreading or misinterpreting the documentation, so please comment if that's the case.

I took a screenshot of the documentation, pointing out what I'm referring to, in case they update it again:

Solution

Use one of the logging libraries that Google supports with a Stackdriver logging transport, like @darshan-devrai's answer. If you don't want to change all your console.log(), console.error(), etc., then just alias the console logger to your logger of choice (similar to this stackoverflow answer).