In my case, there were no backup copies of saves and saves from the Steam cloud were also overwritten with new data.
I really hope that this guide will help you with restoring your saves.
If so, then don’t be lazy and rate it, please.

1. Go to this page.

2. In this page is all your Cloud saves. Find "Payday 2" and press "Show Files" button.


3. On the next page you need to select one of the save files. For example, for Payday 2, saves are stored separately for Linux and Windows. The save for Windows is not suitable for me, since it has already been overwritten with zero progress, but for Linux it was updated a long time ago. I'm downloading it.


4. When I downloaded the file I need to rename it to save098.sav

5. Next I need to go to the Steam save folder. In my case, this is D:\Steam\userdata\12345678\218620\remote.
From this folder you need delete file save098.sav and insert another file from step 4 to replace it.

6. Done. Your progress should now be restored.