### 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
case DAP::ErrorType::NOT_RUNNING:
			error = "not_running";
			error_desc = "Can't attach to a running session since there isn't one.";
			break;
		case DAP::ErrorType::TIMEOUT:
			error = "timeout";
			error_desc = "Timeout reached while processing a request.";
			break;
		case DAP::ErrorType::UNKNOWN_PLATFORM:
			error = "unknown_platform";
			error_desc = "The specified platform is unknown.";
			break;
		case DAP::ErrorType::MISSING_DEVICE:
			error = "missing_device";
			error_desc = "There's no connected device with specified id.";
			break;
		case DAP::ErrorType::UNKNOWN:
		default:
			error = "unknown";
			error_desc = "An unknown error has occurred when processing the request.";
			break;
	}
	message.id = err_type;
	message.format = error_desc;
	message.variables = variables;
	response["message"] = error;
	body["error"] = message.to_json();
	return response;
}
Dictionary DebugAdapterParser::req_initialize(const Dictionary &p_params) const {