Not sure if this helps because it isn't full AKS. Using Azure Container Apps, we have a parent stack that stands up ACA and other things that take more time. Then separate stacks to deploy the applications but since we're using automation-api, deploying an appstack has a programmatic dependency on its parent stack. Pulumi Dungeon has a good example of using automation-api to automate that stack dependency
https://github.com/gitfool/Pulumi.Dungeon