Not sure, if this is a problem with the GOG version of Yakuza 0, or of the game in general:
I noticed, that the Save Game function is a little bit buggy.
About once every 6th or 7th try, the game wont save, even if you pressed all the correct buttons.
You can notice this, that the phrase "Save complete" doesn't appear, although it disappears quickly anyway.
Also the date and time is saved together with the game, so you can check that.
In the first chapters, I lost some game time because of this bug, because I noticed this way too late.
Now I verify the time each time after having saved the game. So if it didn't save, I just try a second time, which normally works fine.
Only one time, I had so "save" three times, until the game finally was saved to disc.
Other than that, the game runs perfectly fine.