How to upgrade PowerShell version

Lately, firing up PowerShell, I noticed that there is a phrase that says:

Install the latest PowerShell for new features and improvements!
https://aka.ms/PSWindows

So why not trying it following the actual Microsoft documentation:

1. I run $PSVersionTable and the version installed is 5.1
2. I run winget search Microsoft.PowerShell and it says that version 7.2 is available as well as the 7.3 preview version
3. I run winget install --id Microsoft.Powershell --source winget and version 7.2 is installed
4. I run $PSVersionTable again and I’m still on 5.1

Let’s try to install it through dotnet:

1. I run dotnet tool install --global PowerShell and the terminal says Tool 'powershell' (version '7.2.6') was successfully installed.
2. I run $PSVersionTable and I’m still on 5.1

I’m following the current Microsoft documentation, where am I wrong?

>Solution :

Powershell 7 (core) is its own application. Search for pwsh.exe and run that