A theoretical question about the UK and Australia

The grass is always greener. Brits are obsessed with Australia and New Zealand with this idealistic view on how life is so much better… I have met so many kiwis and Australians that couldn’t wait to leave and live life in uk in comparison.
I get the impression job opportunities are much better corporately in uk due to London. I’ve also got friends who work in the Australian medical system and brits seem to think it’s all sunshine and rainbows but it’s not much better than our current situation tbh. I will agree pay IS better but then again costs are higher so it needs to be…
I reckon more people would move to Australia just because Brits have this idea portrayed by the media we are the only ones struggling and every other country is near enough a utopia in comparison. A great example of this is the nhs, the shortage on health care workers is not just a uk issue, it’s global. Even in the US where drs are paid insane amounts there is a shortage because the emotional toll of that job is exceptional and no amount of money can compensate some of the things you have to go through.
My close friend who lived in newzealand until she was 18, her parents are English, couldn’t wait to get out. She just said it’s so isolating and so little opportunity for anything yet all I see is British teenagers Romanticising it 🤷🏼*♀️

Now that the UK has left schengen, there are no similar alterantives besides Ireland. But what would happen if Australia and the UK, two very similar countries, established a sort of Schengen area? Would people move from the UK to Australia or from Australia to the UK, do you think?
I don't have the energy to move one centimeter, so this is not for me. I am just curious about which way you think the net migration would go?

As an aside -- the UK has not "left schengen". The UK was never a member of the Schengen Agreement.
You're thinking of the "freedom of movement" part of the EU arrangements, and that's not related to the Schengen Agreement at all. (There are some non-EU countries that are members of Schengen, and some EU countries that are not in Schengen.)
The Schengen agreement means that once you enter the Schengen area, there are no routine border checks when moving within it. But it doesn't mean that you can stay there permanently.