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I saw the blog "Simplify OIDC Trust with the New Pulumi GitHub Action".

Currently, I'm using my PAT to run deployments from a Python script using the Pulumi Automation API. Does the Automation API support OIDC?

Automation API just relies on the pulumi cli, so as long at that is logged in it does not care if the token came via OIDC or is just a static PAT token.  The main question is where are you running your python script, does that environment support oidc? For example, an EC2 instance or lambda both support retrieving an AWS token, and if have a trust relationship setup, you can exchange that token for a Pulumi token via OIDC, and then Automation API will work.