I wanted to say that sounds like too much to make available to web apps at all, but nope, apparently it’s indeed a thing that a website can tell your computer to do[1]. I don’t see an option to do that here either, though. I guess your choices are to submit a pull request[2] adding that capability or to use a manual systemwide toggle (I use Keep Awake![3] on GNOME Shell and Coffee[4] on Android).
[1] https://developer.mozilla.org/en-US/docs/Web/API/Screen_Wake...
[2] https://github.com/captbaritone/webamp
[3] https://extensions.gnome.org/extension/1097/keep-awake/
[4] https://f-droid.org/en/packages/com.github.muellerma.coffee/