### Godot version

4.0.dev (61630d4e1e279278d29576b979b710b9025f473e)

### System information

Windows 10

### Issue description

> **Note**
> this issue was reported by @glimpsebeyond on [godot-vscode-plugin](https://github.com/godotengine/godot-vscode-plugin/issues/389#issuecomment-1302540744)

On Windows, due to a path separator mismatch (Godot: `/` and Windows: `\`), the debug adapter protocol fails as it thinks the opened project is in a different directory.

Likewise, there are other scenarios where this check is too strict, failing as well due to the drive letter's capitalization (`c:\` vs `C:\`. Good example from the linked issue:
```
[error] The editor and client are working on different paths; the client is on 
"d:\gameDev\gd4proj\builder\pawn.cs", but the editor is on "D:/gameDev/gd4proj/builder": CodeExpectedError: 
The editor and client are working on different paths; 
the client is on "d:\gameDev\gd4proj\builder\pawn.cs", but the editor is on "D:/gameDev/gd4proj/builder"
```

### Steps to reproduce

- Try using DAP from a project on Windows (like [VSCode's extension](https://github.com/godotengine/godot-vscode-plugin))

### Minimal reproduction project

N/A
}
	EditorDebuggerNode::get_singleton()->get_default_debugger()->request_stack_dump(frame_id);
	DebugAdapterProtocol::get_singleton()->_current_frame = frame_id;
	body["scopes"] = scope_list;
	return response;
}
Dictionary DebugAdapterParser::req_variables(const Dictionary &p_params) const {
	
	if (DebugAdapterProtocol::get_singleton()->_remaining_vars > 0) {
		return Dictionary();
	}
	Dictionary response = prepare_success_response(p_params), body;
	response["body"] = body;
	Dictionary args = p_params["arguments"];
	int variable_id = args["variablesReference"];
	HashMap<int, Array>::Iterator E = DebugAdapterProtocol::get_singleton()->variable_list.find(variable_id);
	if (E) {
		if (!DebugAdapterProtocol::get_singleton()->get_current_peer()->supportsVariableType) {
			for (int i = 0; i < E->value.size(); i++) {
				Dictionary variable = E->value[i];
				variable.erase("type");
			}
		}
		body["variables"] = E ? E->value : Array();
		return response;
	} else {
		return Dictionary();
	}
}
Dictionary DebugAdapterParser::req_next(const Dictionary &p_params) const {