tugsailor, most "offshore icebreakers" have nozzles. Even the Swedish icebreaking phenomenon Oden features a similar propulsion system as Aiviq. However, nozzles are known to cause problems (clogging) even in diesel-electric Z-drive ships like Fennica and Nordica, so there's a definite loss of overall operational capability in difficult ice conditions especially for conventional shaftline ships that cannot "blow" the nozzles open. This is apparent with Oden when she's being used for escort operations in the Baltic Sea - despite her fame as one of the best icebreakers in the world, she's better off in operations such as the McMurdo break-in and scientific stuff in the Arctic than cutting icebound ships free on the Swedish coast.
As we all know, the advantage of nozzles is that the vessel has much higher bollard pull in open water for towing and anchor-handling operations. Unless you expect to do a lot of ice management and other challenging operations in difficult ice conditions, you're better off with ducted propellers. However, in my opinion azimuth thrusters are something you can't really do without if you want to do serious icebreaking. Perhaps that's why ECO chose them for the two icebreaking AHTS vessels that it was (is?) building...
As for the icebreaking performance, it's possible to calculate a rough estimate based on publicly available technical data and a few drawings from Shell's ice management plan. I might actually have my students use Aiviq in their weekly exercises later this spring. Also, being a new design, it has probably been tested in an ice tank. I would expect that Shell has asked to see the model test report before paying for the vessel.
I, for one, would have wanted to see Aiviq break some ice. When I was up there in 2012, the ice around Kulluk was barely thick enough to walk on.