Is it possible to install Visual Studio in a Windows Container

Visual Studio seems to not be supported officially on Core Server, but I agree it would be really nice to be able to do this. Let's try:

FROM mcr.microsoft.com/windows/servercore:ltsc2019
SHELL ["powershell"]

RUN Invoke-WebRequest "https://aka.ms/vs/16/release/vs_community.exe" -OutFile "$env:TEMP\vs_community.exe" -UseBasicParsing
RUN & "$env:TEMP\vs_community.exe" --add Microsoft.VisualStudio.Workload.NetWeb --quiet --wait --norestart --noUpdateInstaller | Out-Default

RUN & 'C:/Program Files (x86)/Microsoft Visual Studio/2017/Community/MSBuild/15.0/Bin/MSBuild.exe' /version

CMD ["powershell"]

(I'm pushing this image into lukaslansky/visualstudio-netwebworkload, use with caution.)

Output of the build is:

[...]
Microsoft (R) Build Engine version 15.3.409.57025 for .NET Framework
Copyright (C) Microsoft Corporation. All rights reserved.

So this seems to work! You should play with those --add installator arguments to specify what components you need precisely for your build, they correspond to workloads and components you see in the GUI. See the documentation.

Your best bet at this point is to use Visual Studio Build Tools.