Related to this topic # Powershell on Omnia, I can confirm that .NET Core 2.1 & 3.0.0 + PowerShell Core 6.2.1 & 7.0.0 works on Turris Omnia or inside LXC containers, so you can host any ASP.NET Core web application within your Turris Omnia. 
Personally, I am very pleased about this because Bash is driving me crazy.
Tutorials how to install .NET Core to the Turris Omnia LXC container can be found here and for PowerShell Core here.