I am using a similar constellation atm. Instead of building a node package i am building a Docker Image and upload this image to a registry.
I tried different App Service Plans, unfortunately strapi won´t work with the free F1, you have to use at least the B1 plan.
As you can see, i have 2 stages there. One is for the docker image and the other stage is for building and packaging a node solution, which is not tested by me 
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I am using treescale as container registry. there is a free plan with 1 gb for your images. But you can use any container registry you want. The easiest would be to use the Azure Container Registy Service.