I see you're looking to use existing Gamma templates and update content via API. That's a really interesting use case!
Here's where things stand: Right now, the API is create-only. You can generate new presentations from scratch, but there's no remix endpoint yet to take an existing Gamma and modify it. That's why you're not seeing template URL or ID parameters in the docs.
What you CAN do today:
Generate new presentations using your workspace themes
Use the same theme consistently across generations to maintain brand consistency
Pass in your updated content via the inputText parameter
The remix capability is something the team is actively thinking about for future API development, but I can't give you a specific timeline on when it might land. For now, if you need to update existing presentations, you'd need to do that manually in the Gamma app.