Hi Hayok65,
Welcome to Apple Support Communities. I understand that upon connecting your iPhone to the Mac, you're not able to view the available options to mirror the screen of your iPhone to QuickTime. I'll be happy to help.
I recommend to reset both the system management controller (SMC) and the NVRAM (nonvolatile random-access memory). This may help resolve the behavior you're experiencing. Here are two helpful articles with additional details and how to perform each step:
- How to reset the SMC of your Mac
- Reset NVRAM or PRAM on your Mac
In addition, I recommend trying another Lightning to USB cable to see if you're able to mirror the iPhone to QuickTime. This can help isolate this behavior further.
Kind regards.