Looking through these will help. There’s a lot of links to resources through the forum posts here.
https://www.ministryoftesting.com/dojo/lessons/30-days-of-api-testing
For your true struggle, a lot of the posts here will direct you to helpful things.
I can’t really help you with metrics though, since I don’t know what your management might want, I’m more likely to steer you down the wrong path than the right one.