Today I found out that when trying to move an App Service to another App Service Plan (ASP) in Azure there are a few limitations to the portal and its ability to actually move the App Service.

Microsoft states in their docs that the following criteria must be met regarding the two ASPs:

Exists in the same resource group
Exists in the same geographical region
Exists in the same webspace

Sure I thought and created a new ASP. But in an other Resource Group than the original one. When I noticed my error I moved the ASP to the correct Resource Group.

I then tried to move my App Service to the new ASP but was met with the following:
no_app_service_plans_found

I googled around a bit and found an github issue. What is the use of moving of App Service plan if the webspace is not changed? #7281 This Microsoft Employee answered the issue and explained how it worked.

@fschmied You can determine your webspace by going to the properties tab of your web app and checking the FTP URL. The below example FTP URL, waws-prod-bay-033, is the webspace name. You'll need to continue trying again until you have an app service plan with the same webspace.
ftp://waws-prod-bay-033.ftp.azurewebsites.windows.net
For this reason, I would personally recommend you look into using the 'clone app' feature if possible.

Wait what do they actually tell us to remove and create new ASPs and hope that it ends up in the correct webspace. There could be hundreds maybe thousands. There must be a better solution to this. Ofcourse there is, if you just read the documentation correct and actually read the highlighted "notes" you would know that when you create a ASP in the same Resource Group as the ASP you are moving from then you are all set.
note
The secret recipie is to create the ASP in the same resource group with the same region then it gets created in the same webspace. And not as I did it, it does not work when moving a ASP to a resource group.

After you have made the change you can move your new ASP to an other resource group if you want.

So please dont be as dumb as me, read the docs thoroughly and there will be no issues.