iPhone USB C to Lightning Doesn't work!

Clearly there is a problem with the way Apple have designed the USB C connection on the iPhone 15.

I bought the Apple USB C to Lightning converter to try to keep the family connected with most on Lightning. We have an Apple converter on the TV that allows an iPhone with Lightning to display its content through the HDMI lead (Apple lead A1438 - Lightning Digital AV). It works perfectly for everybody else with Lightning ports. But when I use the A2868 converter I get nothing.

I did an Apple chat and they couldn't think of a solution but organised a Genius Bar trip. After an hour of trying the Genius Bar gave up. They tried different iPhone and iPads, changed the lead but all gave the same result. Nothing on the display and the message "not supported"

The HiFi is the same. I have an Apple supplied A1450 that links an Arcam Dock and works perfectly with the Lightning phones. The dock connects and charges the iPhones and is perfect for playing podcasts through the Arcam Solo HiFi. But when I connect the iPhone 15 through the A2868 the dock does not light up to indicate a connected device.

I can't rip these connections out just to suit the iPhone 15 as it wrecks the other family members. Surely there must be a way of mixing old and new iPhones in a real household?

Then the real kicker is the suggested solution from the Genius Bar for the HiFi. Buy a headphone lead for the USB C port. As I had a spare RCA connection I thought that would be creative. But again it didn't work. The iPhone put up a message asking if I was connecting headphones (Yes) but it's totally dead. Not even a sound from the phone speakers so it must be thinking that headphones are connected. Then I got out a pair of wired Bang and Olufsen headphones expecting this lead would work but again nothing. The phone continues to play through its own speakers.

How do I bring family harmony so that Lightning and USB C can coexist in a real family?