### 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
Dictionary event = prepare_base_event(), body;
	event["event"] = "exited";
	event["body"] = body;
	body["exitCode"] = p_exitcode;
	return event;
}
Dictionary DebugAdapterParser::ev_stopped() const {
	Dictionary event = prepare_base_event(), body;
	event["event"] = "stopped";
	event["body"] = body;
	body["threadId"] = 1;
	return event;
}
Dictionary DebugAdapterParser::ev_stopped_paused() const {
	Dictionary event = ev_stopped();
	Dictionary body = event["body"];
	body["reason"] = "paused";
	body["description"] = "Paused";
	return event;
}
Dictionary DebugAdapterParser::ev_stopped_exception(const String &p_error) const {
	Dictionary event = ev_stopped();
	Dictionary body = event["body"];
	body["reason"] = "exception";
	body["description"] = "Exception";
	body["text"] = p_error;
	return event;
}
Dictionary DebugAdapterParser::ev_stopped_breakpoint(const int &p_id) const {