### 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
EditorRunBar::get_singleton()->stop_playing();
	return prepare_success_response(p_params);
}
Dictionary DebugAdapterParser::req_pause(const Dictionary &p_params) const {
	EditorRunBar::get_singleton()->get_pause_button()->set_pressed(true);
	EditorDebuggerNode::get_singleton()->_paused();
	DebugAdapterProtocol::get_singleton()->notify_stopped_paused();
	return prepare_success_response(p_params);
}
Dictionary DebugAdapterParser::req_continue(const Dictionary &p_params) const {
	EditorRunBar::get_singleton()->get_pause_button()->set_pressed(false);
	EditorDebuggerNode::get_singleton()->_paused();
	DebugAdapterProtocol::get_singleton()->notify_continued();
	return prepare_success_response(p_params);
}
Dictionary DebugAdapterParser::req_threads(const Dictionary &p_params) const {
	Dictionary response = prepare_success_response(p_params), body;
	response["body"] = body;
	Array arr;
	DAP::Thread thread;
	thread.id = 1; 
	thread.name = "Main";
	arr.push_back(thread.to_json());
	body["threads"] = arr;
	return response;
}
Dictionary DebugAdapterParser::req_stackTrace(const Dictionary &p_params) const {