Hello, is there a pure golang client to interact with pulumi's REST API?

Not as a public library, there's bits of it in https://github.com/pulumi/pulumi/ and bits in https://github.com/pulumi/pulumi-pulumiservice

Thus the recommended way to talk to the API is to use the SDK which requires pulumi's binary?

Yes, most things you want to query the API for should be exposed by the CLI and then by automation api (but that does currently need the cli installed as well)