Azure DevOps PipeLine MSBuild does not produce web folder like local command

Fairly new to Azure DevOps and PipeLines, but we are stumped by the fact executing an MSBuild command locally or through publish in VS2019 gives us a complete ready to publish folder, while the same command in Azure DevOps pipeline seems to be doing nothing but build.

Local command:

"C:\Program Files (x86)\Microsoft Visual Studio\2019\Enterprise\MSBuild\Current\Bin\msbuild" Webshop\Mvc.csproj /p:PublishUrl="c:\Publish\Mvc" /p:DeployOnBuild=true /p:Configuration=Release /p:WebPublishMethod=FileSystem /p:DeployTarget=WebPublish /p:AutoParameterizationWebConfigConnectionStrings=false /p:SolutionDir="." /p:PrecompileBeforePublish=true

MSBuild task:

steps:
- task: MSBuild@1
  displayName: 'Build solution'
  inputs:
    solution: '$/MVC_Projects/<more here>/Webshop/Mvc.csproj'
    msbuildVersion: 16.0
    platform: '$(BuildPlatform)'
    configuration: '$(BuildConfiguration)'
    msbuildArguments: '/p:DeployOnBuild=true /p:DeployTarget=WebPublish /p:PublishUrl="$(build.artifactstagingdirectory)\publish" /p:WebPublishMethod=FileSystem /p:AutoParameterizationWebConfigConnectionStrings=false /p:PrecompileBeforePublish=true'

We tried playing with the parameters, but that does not seem to have much effect (or we don't know which parameters to tweek). The most we got was adding an /p:DeployTarget=Package and /p:OutDir="$(build.artifactstagingdirectory)\bin" would copy the bin folder. This was still without the .compiled files we were expecting though.

The project is an ASP.NET MVC Framework 4.8 application. The code does build properly and without errors. The logs do not hint with any warning or tasks not being able to be completed, so no clues there. We require the output folder for the full website and not just the DLL's to make our migration to DevOps easier. Having the folder allows other deployment processes to remain the same. This might not be best practice, but it is practical for us at this moment in time.

Question 1. Why is MSBuild doing something else locally than in the DevOps Pipeline? Is it perhaps picking up configuration files we are unaware of ?

Question 2. What settings (or perhaps other task) would we need to set up to get the same local publish folder appear in the $(build.artifactstagingdirectory) folder in DevOps ?

Any insight, direction or solution is appreciated.