No, I cannot reproduce the problem. The jack headphones with the adapter work perfectly for me. As soon as I connect a pair of headphones, the audio signal comes through the headphones. However, the Apple adapter is unfortunately not of particularly high quality. We have already had more than one adapter at home that no longer worked correctly and had similar problems. So the sound was still output via the speakers in the mobile phone.

I would recommend testing the iPhone with another adapter from a colleague. If it works then, the problem is probably due to a faulty adapter. If necessary, try cleaning the plug first. If the adapter is still under warranty, I would register it for warranty. Otherwise, buy a new one.

And yes, in short: Apple seems to want you to use your headphones with Bluetooth. They like to sell you the Apple Airpods the best. That seems to work well for that so far.