Hi @Kristofer Tvedt Henrichsen ,
Perhaps you can elaborate on the need to have a new app service with each deployment because it's certainly an uncommon workflow. Nonetheless, I think you can achieve your goal by making use of ARM templates inside a PowerShell script. You can create your template where the build version of your CI build is a parameter to your CD. This parameter can be passed into your *.ps1 that will use it to create your app service in which resource group you want. Your script files can be kept inside the repo to make referencing them in the pipeline easier. This doc illustrates using yaml to define your pipeline and references a PowerShell script file. This blog post shows how to use a script file in a CI/CD pipeline with tasks. You can easily export your resources to get a template that you can modify to accept parameters from your pipeline.
I hope this helps point you in the right direction.