How can I update the styles of a class?

To get the rule with that class use CssComposer.getRule and once you have the rule update its style

const rule = editor.CssComposer.getRule('.btn_hovered');
rule && rule.addStyle({ color: 'red' });

@artf Hi, I am trying to access with that statement, but I get null as a response, what could be the issue?

Well, the rule should be there at first. If you're using canvas.styles option in your init method those are not appended inside CssComposer, so you have to add it first.