I recently bought a Moto G Power 5g 2024 and I'm really happy with it. No headaches/nausea/tinnitus.
Here's the waveform using the Thorlabs PDA100A2. I went to a couple different stores (Best Buy and Microcenter) and tested about 50 phones and this was the best Android phone (i.e., lowest flickering) I could find.

No PWM at any brightness level.
There were a couple iPhones with a relatively smooth waveform (iPhone SE 3rd Gen and iPhone XR 4G), but I prefer an Android so I didn't look too closely at those.