I don’t think the country of Israel is explicitly doing the manipulating, I think one country’s allies are just statistically richer and more influential than the other
In the case of Australia you're correct in that it's not Israel reaching into Australia to alter opinion.
What is the case (in a many layered complex fabric) is that Australian Jewish groups have both actively pushed a narrative and worked hard to discredit any inkling of voice given to Palenstine by the public broadcaster that does work hard to be in the vicinity of neutral.
For better or worse they have gamed the Australian media system in their favour.
This recently hit the Federal Court of Australia which determined that (former) ABC executives (senior staff of the public broadcaster) caved to a pressure campaign to fire a radio broadcaster who tweeted a link to a Human Rights Watch report (that was unfavourable to Isreal) "in her own time" (not on the public clock and not contrary to any employment agreement).
