### 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
#include "debug_adapter_parser.h"
#include "editor/debugger/editor_debugger_node.h"
#include "editor/debugger/script_editor_debugger.h"
#include "editor/export/editor_export_platform.h"
#include "editor/gui/editor_run_bar.h"
#include "editor/plugins/script_editor_plugin.h"
void DebugAdapterParser::_bind_methods() {
	
	ClassDB::bind_method(D_METHOD("req_initialize", "params"), &DebugAdapterParser::req_initialize);
	ClassDB::bind_method(D_METHOD("req_disconnect", "params"), &DebugAdapterParser::req_disconnect);
	ClassDB::bind_method(D_METHOD("req_launch", "params"), &DebugAdapterParser::req_launch);
	ClassDB::bind_method(D_METHOD("req_attach", "params"), &DebugAdapterParser::req_attach);
	ClassDB::bind_method(D_METHOD("req_restart", "params"), &DebugAdapterParser::req_restart);
	ClassDB::bind_method(D_METHOD("req_terminate", "params"), &DebugAdapterParser::req_terminate);
	ClassDB::bind_method(D_METHOD("req_configurationDone", "params"), &DebugAdapterParser::prepare_success_response);
	ClassDB::bind_method(D_METHOD("req_pause", "params"), &DebugAdapterParser::req_pause);
	ClassDB::bind_method(D_METHOD("req_continue", "params"), &DebugAdapterParser::req_continue);
	ClassDB::bind_method(D_METHOD("req_threads", "params"), &DebugAdapterParser::req_threads);
	ClassDB::bind_method(D_METHOD("req_stackTrace", "params"), &DebugAdapterParser::req_stackTrace);
	ClassDB::bind_method(D_METHOD("req_setBreakpoints", "params"), &DebugAdapterParser::req_setBreakpoints);
	ClassDB::bind_method(D_METHOD("req_breakpointLocations", "params"), &DebugAdapterParser::req_breakpointLocations);
	ClassDB::bind_method(D_METHOD("req_scopes", "params"), &DebugAdapterParser::req_scopes);
	ClassDB::bind_method(D_METHOD("req_variables", "params"), &DebugAdapterParser::req_variables);
	ClassDB::bind_method(D_METHOD("req_next", "params"), &DebugAdapterParser::req_next);
	ClassDB::bind_method(D_METHOD("req_stepIn", "params"), &DebugAdapterParser::req_stepIn);
	ClassDB::bind_method(D_METHOD("req_evaluate", "params"), &DebugAdapterParser::req_evaluate);
	ClassDB::bind_method(D_METHOD("req_godot/put_msg", "params"), &DebugAdapterParser::req_godot_put_msg);
}
Dictionary DebugAdapterParser::prepare_base_event() const {