I've just updated my phone to an iPhone 16 so I've got the same problem of figuring how to connect a Sonic Port (non-VX) with a Lightning cable to a phone with a USB-C socket.
I tried an MFA certified Lightning (socket) to USB-C adapter but it didn't work. When I looked more closely at the listing for it on Amazon I realised that although it said it was compatible for "power and data", it didn't say anything about audio. There appear to be four different levels of functionality with Lightning adapters: power, data, earphones, and audio. It's the last one that's relevant for the Sonic Port, I think.
So I bought the official Apple adapter, "USB-C to Lightning Adapter". (priced at 29 GBP in the UK or 29 USD in the US), and it works fine with my iPhone 16. The Sonic Port is recognised and just works with all the software I tried: Mobile POD, AmpKit, BIAS AMP, JamUp Pro.
https://www.apple.com/shop/product/MUQX3AM/A/usb-c-to-lightning-adapter
https://support.apple.com/en-us/109044
IIRC, when the iPhone 15 launched there was discussion about the fact that it implemented more "standard" USB-3 functionality than previous Apple USB-C mobile devices, i.e. iPads. So this may explain why the Apple adapter works with my iPhone but it isn't working for CE_123 and his iPad.