Just a comment from a renter who used to have a cockatiel. The cockatiel was fine for a long time until I moved in with my gf, who the cockatiel saw as competition (I’d had the cockatiel for about 10 years at this point). The noise was terrible although we did our best to minimise it for other people. What ended up being effective was to take ourselves and the cockatiel to an avian vet experienced in behavioural issues – there are a few around Sydney and I believe even a few non-vet people who specialise in bird/parrot behaviour. After ruling out health problems that could be causing the annoying behaviour, we were given some advice on what could help the noise problem (and other anti-social cockatiel behaviour). After following the vet’s advice, it wasn’t too long before the problem was minimised and we were all happy again.
Perhaps suggesting this to your neighbour with a suggested list of contacts(just google ‘avian vet sydney’)? I realise that the bird may not be allowed to be there, but this might be a solution that keeps everyone happy (including the lonely bird).