Why is C# autocomplete working?
The autocompletion you see is working via the default C# tooling for Visual Studio Code, on which Godot .NET Tools relies.
Why does it say disconnected?
The disconnected message is from the extension godot-tool. Read the popup, it says source: godot-tool.
Do not confuse godot-tool with Godot .NET Tools.
The godot-tool extension provides support for GDscript using the Godot language server. And it is not connecting, see below for what you need to make it connect.
How to make it connect?
To connect godot-tool you need to make sure:
The language server port match. You find the language server port configuration under Editor Settings -> General -> Network -> Language Server.
Looking at your picture, it seems you have configured the debugger port instead of the language server port.
You will have to configure a different port for the debugger, so they don't conflict.
The connection is not being taken by something else. When the connection is taken Godot will output a message (
[LSP] Connection Taken). If you see it and godot-tool is disconnected, it means something else connected instead.
If the port matches and nothing else took the connection, click "Retry" on the godot-tool popup.
Also note that Godot - by default - will advance the port number if you are running multiple instances of the editor (the first gets the confugured port, and the next instance one gets the next port number and so on).
If the port does not match because there were multiple instances running, or it didn't not match and you fixed it, or if the connection was taken by something else, youelse… You might have to restart Godot for it to be able to connect again.
By the way, C# Tools for Godot and godot-tool are the extensions made by the core Godot developers.
Godot .NET Tools is a third party alternative for C# with Godot. I have not compared it to C# Tools for Godot, but if Godot .NET Tools is causing problems, consider switching to C# Tools for Godot.
By the way, 4.0 is no under support. So if you run into issues with it, do not expect any fixes. Thus, consider updating your Godot version. 4.1 is the lower supported 4.x version at the time of writing.
Ignoring the connection issue
If ultimately the connection does not work, go ahead and click Ignore on the pupup. This means you will not have autocomplete and debugging for GDScript on Visual Studio Code. But since you are using C# instead, that might be acceptable.
Futhermore, you should be able to use C# without godot-tool at all. So you might even disable or uninstall godot-tool entirely.