Can I update a JSF component from a JSF backing bean method?

Using standard JSF API, add the client ID to PartialViewContext#getRenderIds().

FacesContext.getCurrentInstance().getPartialViewContext().getRenderIds().add("foo:bar");

Using PrimeFaces specific API, use PrimeFaces.Ajax#update().

PrimeFaces.current().ajax().update("foo:bar");

Or if you're not on PrimeFaces 6.2+ yet, use RequestContext#update().

RequestContext.getCurrentInstance().update("foo:bar");

If you happen to use JSF utility library OmniFaces, use Ajax#update().

Ajax.update("foo:bar");

Regardless of the way, note that those client IDs should represent absolute client IDs which are not prefixed with the NamingContainer separator character like as you would do from the view side on.

I also tried to update a component from a jsf backing bean/class

You need to do the following after manipulating the UI component:

FacesContext.getCurrentInstance().getPartialViewContext().getRenderIds().add(componentToBeRerendered.getClientId())

It is important to use the clientId instead of the (server-side) componentId!!