How to set the Pipeline + Stage through the API

Hey there,

The API endpoints for /v1/pipelines/$id specifies that one can send a patch request with a pipelines and a pipeline stage. However, each pipeline is a copy of template pipeline for one specific opportunity. So I'm wondering: if an opportunity doesn't have a pipeline set: how can I set the Pipeline and stage? (I tried setting one of the pipelines I knew from another opportunity but that didn't work. Would it be possible to put something like that into the main product (e.g. a setting "if an opportunity is created in category X without a pipeline, it is put into that stage of that pipeline").?

Best,

Pascal