Koen Verbeeck leaves the confines of Microsoft Fabric:
In the blog post Call a Fabric REST API from Azure Data Factory I explained how you can call a Fabric REST API endpoint from Azure Data Factory (or Synapse if you will). Let’s go a step further and execute a Fabric Data Pipeline from an ADF pipeline, which is a common request. A Fabric capacity cannot auto-resume, so you typically have an ADF pipeline that starts the Fabric capacity. After the capacity is started, you want to kick-off your ETL pipelines in Fabric and now you can do this from ADF as well.
Click through for the process. Though do check the warnings that Koen offers around either spending extra money by remaining in synchronous execution mode, or always getting a positive result in asynchronous execution mode, regardless of whether the underlying Fabric Data Pipeline worked or not.