Intellisense (Autocompletion) is a pure workflow of .Net Environment. So, you need to have .Net 'Developer pack' (not Runtime) installed on your system as it installs all three necessary components below:
- .Net framework
- .Net Target pack
- .net SDK
reference link: https://dotnet.microsoft.com/download/visual-studio-sdks
It is directly installed to a system admin-accessible path, so no need setting it up. Now, you have to tell VS Code which .Net version to use (whichever you have installed).
Your Unity project will have these two files in the root directory:
- Assembly-CSharp.cs
- Assembly-CSharp-Editor.cs
In these both files search for line (probably 16):
<TargetFrameworkVersion>v4.8</TargetFrameworkVersion>
Edit version that you had just installed (I had 4.8). Then reopen VS Code. Now everything should work fine.