This is from Mint 22. MS does have its own PPA though.
$ apt search dotnet
p dotnet-apphost-pack-6.0 - Internal - targeting pack for Microsoft.NET
p dotnet-apphost-pack-7.0 - Internal - targeting pack for Microsoft.NET
p dotnet-apphost-pack-8.0 - Internal - targeting pack for Microsoft.NET
p dotnet-host - dotNET host command line
p dotnet-host-7.0 - dotNET host command line
p dotnet-host-8.0 - .NET host command line
p dotnet-hostfxr-6.0 - dotNET host resolver
p dotnet-hostfxr-7.0 - dotNET host resolver
p dotnet-hostfxr-8.0 - .NET host resolver
p dotnet-runtime-6.0 - dotNET runtime
p dotnet-runtime-7.0 - dotNET runtime
p dotnet-runtime-8.0 - .NET runtime
p dotnet-runtime-dbg-8.0 - .NET Runtime debug symbols.
p dotnet-sdk-6.0 - dotNET 6.0 Software Development Kit
p dotnet-sdk-6.0-source-built-arti - Internal package for building dotNet 6.0 So
p dotnet-sdk-7.0 - dotNET 7.0 Software Development Kit
p dotnet-sdk-7.0-source-built-arti - Internal package for building dotNet 7.0 So
p dotnet-sdk-8.0 - .NET 8.0 Software Development Kit
p dotnet-sdk-8.0-source-built-arti - Internal package for building the .NET 8.0
p dotnet-sdk-dbg-8.0 - .NET SDK debug symbols.
p dotnet-targeting-pack-6.0 - Internal - targeting pack for Microsoft.NET
p dotnet-targeting-pack-7.0 - Internal - targeting pack for Microsoft.NET
p dotnet-targeting-pack-8.0 - Internal - targeting pack for Microsoft.NET
p dotnet-templates-6.0 - dotNET 6.0 templates
p dotnet-templates-7.0 - dotNET 7.0 templates
p dotnet-templates-8.0 - .NET 8.0 templates
p dotnet6 - dotNET CLI tools and runtime
p dotnet7 - dotNET CLI tools and runtime
p dotnet8 - .NET CLI tools and runtime
p libgtk-dotnet3.0-cil - GTK.NET library
p libgtk-dotnet3.0-cil-dev - GTK.NET library - development files
dotnet-sdk-8.0 should have the rest of what you need downstream from there. For other libraries and versions, you should be able to use NuGet with your project directly.
I've been using the script installer version intended for ci/cd as I actually like that installer more, it's the only one that really supports multiple versions correctly.
It's not. Microsoft provides its own apt repository you need to add first.