Is there official documentation of the steps necessary to allow Power Automate to call Azure Cognitive Search that is exposed only by a private endpoint?
If you need a solution right now, I would advise installing the on prem data GW on a VM in a network zone that can access your private endpoint.
https://learn.microsoft.com/en-us/power-apps/maker/canvas-apps/gateway-reference
In the longer term, this will probably be supported more natively when custom connectors are on boarded to subnet delegation:
https://learn.microsoft.com/en-us/power-platform/admin/vnet-support-overview
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