You can check whether your controller is detected by visiting https://gamepad-tester.com/. Note that you have to operate one of the buttons for the site to recognize your controller. If it is detected, that confirms that the ChromeOS and browser support the controller.
In addition to being detected, a controller must use a standard mapping to be usable with GeForce NOW. You can check this by seeing if the mapping field reports standard. Controllers that do not use standard mapping are not currently supported. You can check the mapping of different controls as seen by the browser on this website as well. You can expect the same mapping to apply while you are on https://play.geforcenow.com.
You can also see the input devices on ChromeOS by following these steps
1. Visit chrome://system.This will gather lots of system-level logging and present it in a more easily digested form.
2. Open the page and navigate to the input_devices section - the list is ordered alphabetically.
3. Expand this node, and you will see all of the connected input devices; it will include many devices you wouldn't normally expect, such as a laptop lid switch and a power switch.
4. Look through this list for anything with a Controller or Gamepad in the name, and confirm that this is your controller.