### 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 req_restart(const Dictionary &p_params) const;
	Dictionary req_terminate(const Dictionary &p_params) const;
	Dictionary req_pause(const Dictionary &p_params) const;
	Dictionary req_continue(const Dictionary &p_params) const;
	Dictionary req_threads(const Dictionary &p_params) const;
	Dictionary req_stackTrace(const Dictionary &p_params) const;
	Dictionary req_setBreakpoints(const Dictionary &p_params) const;
	Dictionary req_breakpointLocations(const Dictionary &p_params) const;
	Dictionary req_scopes(const Dictionary &p_params) const;
	Dictionary req_variables(const Dictionary &p_params) const;
	Dictionary req_next(const Dictionary &p_params) const;
	Dictionary req_stepIn(const Dictionary &p_params) const;
	Dictionary req_evaluate(const Dictionary &p_params) const;
	Dictionary req_godot_put_msg(const Dictionary &p_params) const;
	
	Dictionary ev_initialized() const;
	Dictionary ev_process(const String &p_command) const;
	Dictionary ev_terminated() const;
	Dictionary ev_exited(const int &p_exitcode) const;
	Dictionary ev_stopped_paused() const;
	Dictionary ev_stopped_exception(const String &p_error) const;
	Dictionary ev_stopped_breakpoint(const int &p_id) const;
	Dictionary ev_stopped_step() const;
	Dictionary ev_continued() const;
	Dictionary ev_output(const String &p_message) const;
	Dictionary ev_custom_data(const String &p_msg, const Array &p_data) const;
	Dictionary ev_breakpoint(const DAP::Breakpoint &p_breakpoint, const bool &p_enabled) const;
};
#endif