Currently I only see MySQL errors and user connections being logged. How can I enable more detailed logs in order to generate metrics?
Ah okay, those metrics are stored in the database itself, not logged. Which makes more sense, but it was just a bit hidden where the Cloud Console was exposing them.
In your list of Cloud SQL instances, instead of clicking into an instance, you want to select the checkbox next to the instance, which will bring up an "Info" panel on the right, from which you can select different metrics.
I'm guessing these metrics don't integrate into the Metrics Explorer.