Concerned about layover time in German airports for trip to Japan

That looks like a single Star Alliance itinerary. If it's all booked on a single ticket, you should be fine. Your bags will get checked through to your final destination and these are okay transit times, since you only need to get to the next gate. Munich is a little tight since it's a large airport and smaller flights often use buses and not a jet bridge. However, if you miss it, the airline will just put you on the next flight at no cost.

If this is on separate tickets, you are out of luck. You have to collect your bags, leave the secure area, check in at the counter, drop off your bags again, get back through security to the gate. You may be able to make the connection in Stuttgart, if you are really lucky, but the Munich one is almost impossible.

If the itinerary was booked through a halfway competent travel agent (or booked all at once, say, from Lufthansa's website), then it will be on a single ticket, and you shouldn't have any problems.

Your bags should be checked through all the way to Osaka, and you won't even see them during the layovers.

You will pass through Schengen passport control -- but not security -- in Stuttgart, Frankfurt and Munich. If you have a Croatian passport, this should be painless.

The main risk would be that the flight from Stuttgart to Frankfurt gets significantly delayed (or you're delayed into Stuttgart). If you don't make the connecting flight, the airline will rebook you on a later flight at no cost. You might still lose a day of your vacation, of course, but no amount of slack in the itinerary can completely guard against that.