The Aux switch needs to be hard wired to the blue switch. A physical wire is connected using the traveller port. If you want a “wireless” 3way setup, then a second blue switch must be used and connected either through binding or through automation.
Since you’re using hue bulbs in room 2, if you are able to make that physical connection between the blue switch in room 1 and the aux switch in room 2, then you could use automations to control those hue bulbs through something like a double tap. I can’t see these switches being wired this way though, and the cost and effort of re-wiring is probably going to be more than just putting in a second blue switch.