Custom pipeline/job flag/tag/badge thing

Custom job flag/tag/badge thing (don’t know what it’s called)

Is it possible to set up custom colored tags on jobs and/or pipelines? I don’t know what they’re called - and hence wasn’t able to properly search - but I’m talking about the latest on green, detached on blue, etc, under the pipeline ID in the pipeline page, e.g. there: https://gitlab.com/gitlab-org/gitlab/-/pipelines

Specifically, I’d like two things:

  1. Being able to configure custom versions of those, for example to show visually why a pipeline failed. So do something like if this job fails => show this colored thingy
  2. Have one for pipelines triggered remotely, by a call to the API with a trigger token, to be able to quickly identify how a pipeline was triggered.

I guess just the name of those things, to help me research by myself, would be enough to answer my question. Thanks!