Huvebusters. One save per chapter? (Gears 5)

He started on Madness, got to the second chapter, met the first heavy boss, decided to kill him later. Before that, he died many times, the saves worked. But as soon as you quit the game - the chapter goes AGAIN! For some reason, at the same time, the collectibles collected in the first chapter did not get into the general statistics either, as if I did not collect them. Is this game buggy or is it right? You understand that on Madness with a risk at any time, there is no point in starting a chapter from the very beginning. And I don’t want to play on others. So either I delete, or I still find a solution to the problem. What do you think?