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What do you mean by "standalone"?

Please ignore that (have edited the message as well). I ended up creating Pulumi.AzureNative.Web.WebApp with Kind="functionapp" instead and it worked. Just got to figure out how to link the function itself to the functionapp on deployment.

That's what I would have replied with if I'd better understood your original question. An actual "function" will appear in the function app when the function is deployed to that specific function app / app service. We deploy ours from Github Actions. But you could deploy it via a publish profile from the function app. Pulumi itself isn't required as part of deploying a function to a function app.

Indeed, im using a yml publish profile for the static app but somehow it does not get deployed even though the pipeline compiles the api. Was yours a static web app with a function api as well?

No. I've done static web apps in Azure, but not via Pulumi - last I checked there was some friction in doing that b/c of the way Azure initially connects a static web app to GitHub. I've done a number of Azure function apps via Pulumi, and they've always just worked - both for creating the function app and for deploying to them via GitHub Actions.