How long a completed Project Habakkuk might survive

If Churchill had completed HMS Habakkuk, what air group would it carry and how long could it survive after 1945?

It could operate very heavy aircraft and remain useful well into the postwar period if its refrigeration and power systems were maintained, possibly with nuclear propulsion.

In this counterfactual, Habakkuk is imagined as a huge floating assembly of pykrete sections rather than a conventional ship. Its air group could include Lancasters and strike fighters, with room to operate very heavy aircraft. The structure is considered partly self-maintaining provided its systems remain working. It is therefore expected to last well beyond 1945, to Soviet discomfort. Nuclear propulsion is suggested as a later possibility.