The Phone Itself (Refresh Rate & Touch Sampling Rate)
Smoothness on screen and responsiveness under your finger are two different numbers.
What it changes
Refresh rate (60 Hz, 120 Hz and so on) is how many times per second the screen redraws — that is visual smoothness. Touch sampling rate is how many times per second the panel reads your finger, and that is responsiveness. They get confused constantly, but in a game like Honor of Kings, where finger movement *is* the input, the second one is what you feel. There is also an in-game setting: a high-refresh phone does nothing until you raise the frame-rate option inside the game.
What to look at
Touch sampling rate is often missing from spec sheets, so a phone that publishes it is a safer bet. Whether the phone has real cooling hardware (a vapour chamber, for instance) ties directly to the heat entries above. A bigger screen reduces mis-taps up to the point where your hand stops reaching. Before replacing anything, check that the in-game frame-rate setting on your current phone is already turned up. If frames are not dropping, replacing the phone comes last — cooling and network are cheaper suspects.