@Alexey-T Before I provide a fix, could you please do a test to make sure that the error exists?

All you need is, using fpc, to create a python engine at MacOS64 / Linunx 64, call
PyInt_FromLong and
PyInt_AsLong
and check whether they provide the correct results..

Ok
In Lazarus console demo, I did

procedure TfmMain.PythonEngineAfterInit(Sender: TObject);
const
  NTest: Longint = 1 shl 30;
var
  dir: string;
begin
  dir:= ExtractFilePath(Application.ExeName);
  {$ifdef windows}
  Py_SetSysPath([dir+'DLLs', dir+cPyZipWindows], false);
  {$endif}
  Py_SetSysPath([dir+'Py'], true);

  Caption:= BoolToStr(PythonEngine.PyInt_AsLong(PythonEngine.PyInt_FromLong(NTest)) = NTest, true);
end;  

app start in Ubuntu 20 x64 - caption is True

(Ubuntu has Py 3.8)

Thanks. Could you please try the following:

var
  P1, P2: PPyObject;
with PythonEngine do begin
  P1 := PyInt_AsLong(1);
  P2 := PyNumber_Negative(P1);
  Assert(PyInt_AsLong(P2) = -1);
end;

@Alexey-T So what is the verdict?

I was busy, will test today

It didnt compile, fixed to

  with PythonEngine do begin
    P1 := PyInt_FromLong(1);
    P2 := PyNumber_Negative(P1);
    Assert(PyInt_AsLong(P2) = -1);
  end; 

and it runs OK here.
no error.

@Alexey-T
Is your fpc program 64 bits?
Very weird:
https://usrmisc.wordpress.com/2012/12/27/integer-sizes-in-c-on-32-bit-and-64-bit-linux/
https://en.wikipedia.org/wiki/64-bit_computing#64-bit_data_models
https://stackoverflow.com/questions/35844586/can-i-assume-the-size-of-long-int-is-always-4-bytes
and other documentations say that, in Linux and MacOS 64bits, long is 8 bits (like Int64).
FPC longInt is 4 bits everywhere. Can you confirm that?

The discrepancy should cause the above to fail. Shouldn't it?
Any thoughts?

Unless fpc takes account of that and does automatic conversions. Does looking at the generated assembly code shed some light?

@Alexey-T

Could you please try the following as well:

  with PythonEngine do begin
    P1 := PyInt_FromLong(-1);
    P2 := PyNumber_Negative(P1);
    Assert(PyInt_AsLong(P2) = 1);
  end; 

Yes, it is Linux x64, Py 3.8.
Last snippet also works ok! ie no exception. even BoolToStr() shows True.

@Alexey-T Can you confirm that FPC longInt is 32 bits (4 bytes) in Ubuntu 64 bits?
Shall I close this issue then?

It shows 4

procedure TForm1.FormCreate(Sender: TObject);
begin
  caption:= inttostr(sizeof(Longint))
end;
       

ubuntu x64

App is for linux x64

@Alexey-T Could you please try the above tests on a Mac, so that I can close the issue.