### 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
idx = i;
					break;
				}
			}
		} else if (platform_string == "web") {
			for (int i = 0; i < EditorExport::get_singleton()->get_export_platform_count(); i++) {
				if (EditorExport::get_singleton()->get_export_platform(i)->get_name() == "Web") {
					idx = i;
					break;
				}
			}
		}
		if (idx == -1) {
			return prepare_error_response(p_params, DAP::ErrorType::UNKNOWN_PLATFORM);
		}
		EditorRunBar *run_bar = EditorRunBar::get_singleton();
		Error err = platform_string == "android" ? run_bar->start_native_device(device * 10000 + idx) : run_bar->start_native_device(idx);
		if (err) {
			if (err == ERR_INVALID_PARAMETER && platform_string == "android") {
				return prepare_error_response(p_params, DAP::ErrorType::MISSING_DEVICE);
			} else {
				return prepare_error_response(p_params, DAP::ErrorType::UNKNOWN);
			}
		}
	}
	DebugAdapterProtocol::get_singleton()->get_current_peer()->attached = false;
	DebugAdapterProtocol::get_singleton()->notify_process();
	return prepare_success_response(p_params);
}
Dictionary DebugAdapterParser::req_attach(const Dictionary &p_params) const {