As of Chrome OS 85, anyone can use a high refresh rate display with their Chromebook just by selecting it in the settings
Open Settings
Click on Device in the side menu.
Select Displays.
Use the Refresh Rate dropdown box to choose your desired figure.
You'll have a chance to confirm that you're happy with the change then or revert back to whatever you were on before if you're not
also worth noting for this wee tip
The display connected directly from the HDMI output is only capable of going up to 120Hz
The display connected over USB-C to HDMI can go up to the full 144Hz.
So, just as on Windows or Mac, the hardware on the Chromebook or Chromebox will very much decide on how high you can turn up your refresh rate