I don't know if the iPhone 14 Pro Max supports 120 Hz refresh rates on external displays. I suspect not.
The iPhone 14 Pro Max does have "ProMotion technology with adaptive refresh rates up to 120Hz" – which means that the refresh rate for the built-in screen can be as high as 120 Hz at times. My understanding is that the iPhone does not run at 120 Hz all the time, but may vary the refresh rate to save power and reduce heat generation when redrawing slowly-changing content that does not really need such a high refresh rate.
iPhone 14 Pro - Technical Specifications - Apple Support
For a cabled video connection, the iPhone 14 Max supports "Up to 1080p through Lightning Digital AV Adapter and Lightning to VGA Adapter (adapters sold separately)".
The description of the Lightning Digital AV Adapter (Lightning to HDMI) does not mention a maximum refresh rate, and I suspect that the maximum refresh rate is either 30 Hz or 60 Hz. Even the newer adapter that Apple sells for USB-C-equipped Macs and iPads might top out at 60 Hz.