Apparently there is no pure WPF bindings by Microsoft, but as mentioned before you can use one of third-party implementations.
Alternatively, you can do it by yourself from the scratch:

It all boils down to WinAPI calls:
https://learn.microsoft.com/en-us/windows/win32/api/shellapi/nf-shellapi-shell_notifyicona?redirectedfrom=MSDN
Those are C# bindings for those WinAPI functions:
https://www.pinvoke.net/default.aspx/shell32/Shell_NotifyIcon.html?diff=y