I have found the issue and it was plain stupidity and lack of focus.

The cursor DOES WORK always, being hidden, shown using loadscreen_cursor 'yes', or using a custom cursor.
I was missing this file definition on my fxmanifest.lua:

...
file 'assets/music.mp3'
file 'assets/images/sound-on.png'
file 'assets/images/sound-off.png'
file 'main.js'    <--------- was missing this line
file 'style.css'
file 'index.html'
...

After this, as expected, the event handlers loaded properly and mouse events such as mousemove and click started being responded to