I don't think there's any objective measure by which software has not become more complex over time.
The uefi bootloader contains more code and complexity than your average 90s OS. Your smartphone is running at least two, possibly more operating systems. Desktop software of the past decades did not have to deal with even a fraction of the security considerations of even a simple web app. The base runtime of your typical managed language alone is more complex than complex desktop apps of the past.
> How are you supposed to check if it really does that if you haven't got the slightest idea about programming?
This one is easy: you check if its output matches your expectation. In the same way you don't need to know how to program a calculator in order to use one.
If you want to get fancy, you could even ask it to encode your expectations as a test suite.
You may be surprised to hear that a large amount, maybe even the majority, of academic research does not use source control, unit testing, etc, yet they still manage to get work done.
I've even encountered this in industrial research from teams in large companies that you'd expect to know better...