Azure AI Foundry/Azure AI Service - cannot access agents

I'm struggling with getting agents to work via API which were defined in AI Foundry (based on Azure AI Service).

When defining agent in project in AI Foundry I can use it in playground via web browser. The issue appears when I'm trying to access them via API (call from Power Automate). When executing Run on agent I get info that agent cannot be found.

The issue doesn't exist when using Azure OpenAI and defining assistants. I can use them both via API and web browser.

I guess that another layer of management which is project might be an issue here. I saw usage of SDK in Python and first call is to connect to a project and then get an agent.

Does anyone of you experienced the same? Is a way to select and run agent via API?