Fluent Bit docker input plugin doesn't output metrics in kubernetes (AWS EKS)

Question

I have a Kubernetes cluster running in AWS (EKS) with some pods running in it. I would like to use Fluent Bit to fetch (not only logs) but also metrics from the pods/containers.

The logging works fine (I use the tail input plugin for that). But the metrics doesn't work when I use the Docker Input plugin with the following configuration:

[INPUT]
  Name docker
  Interval_Sec 5
  Tag metric.*

[OUTPUT]
  Name stdout
  Match metric.*