### 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"] = "output";
	event["body"] = body;
	body["category"] = "stdout";
	body["output"] = p_message + "\r\n";
	return event;
}
Dictionary DebugAdapterParser::ev_breakpoint(const DAP::Breakpoint &p_breakpoint, const bool &p_enabled) const {
	Dictionary event = prepare_base_event(), body;
	event["event"] = "breakpoint";
	event["body"] = body;
	body["reason"] = p_enabled ? "new" : "removed";
	body["breakpoint"] = p_breakpoint.to_json();
	return event;
}
Dictionary DebugAdapterParser::ev_custom_data(const String &p_msg, const Array &p_data) const {
	Dictionary event = prepare_base_event(), body;
	event["event"] = "godot/custom_data";
	event["body"] = body;
	body["message"] = p_msg;
	body["data"] = p_data;
	return event;
}