That is a very specific form of refresh token but not the only model. You can just easily have your "API key" be that refresh token. You submit it to an authentication endpoint, get back a new refresh token and a bearer token, and invalidate the previous bearer token if it was still valid. The bearer token will naturally expire and if you're still using it, just use the refresh immediately, if its days or weeks later you can use it then.

There doesn't need to be any OIDC or third party involved to get all the benefits of them. The keys can't be used by multiple simultaneous clients, they naturally expire and rotate over time, and you can easily audit their use (primarily due to the last two principles).