It's due to different reasons, but very little to do with car manufacturing.

Cities in Europe are blessed and cursed with being established long before cars. This makes it expensive to expand the roads, and it is also difficult to increase the size of cities outwards, because there's not a lot of available land anywhere. So when populations increases, it makes sense to make public transport better, because it's the cheaper and only option.

It's not all good though. Only the largest cities have good public transport. Smaller towns are increasing outwards because rural land is cheaper. Parking is limited or costly in the centres, so people drive out of the town for shopping where parking is free and easy. This kills the businesses in small town centres despite their population growth. A large group of the population living outside the capitals is currently getting more and more car dependent, not by choice, but by necessity.

Japan is different. They simply planned ahead and invested heavily in public transport in the years after the war, 1947-1987 before their population grew. They literally built railroads and the Tokyo metro before it was needed. With huge success. The cities grew with the public transport.

Another historical difference is that while both European and Japanese public transport started as government projects and both have since been privatized, the fragmentation in European states and municipalities have made it difficult to do in a profitable way. It's usually government subsidized, and therefore still depending on local political will to budget for it, while the larger Japanese railway companies are (somewhat) less dependent on local political budgets. In short: JR rail can more easily add another departure if they think it makes sense, whereas a European railroad company would need to know how much the government is willing to pay for having more departures etc.

I do have hopes that Europe will catch up again, because the long term environmental pledges are pushing politicians in the right direction. It's no longer enough to only consider the cost and corporate interests. The people want less pollution and traffic and vote accordingly.