How Commonwealth navies already supported the Falklands campaign

How would the Falklands War change if Canada, Australia, and New Zealand were still formally part of the Empire?

Not dramatically, because they already supported British deployments indirectly, though a formal empire might send some of their ships south in person.

Canada, Australia, and New Zealand are described as contributing indirectly by covering deployments elsewhere and offering assistance. If they remained within a more formal imperial structure, some ships might sail directly to the South Atlantic. The wider strategic effect would still resemble the historical redistribution of allied naval responsibilities. The answer distinguishes visible participation in the task force from the less visible support that frees British ships for combat.