I just wanted to contribute to this thread because I referred to it multiple times and found it very helpful. My scenario was: applied for release through ATO on 9/10, superfund website showed transfer of money out of my super account on 18/10, MyGov account (underneath 'status' table) showed a message saying 'amount transerred to you' on 23/10. From start to finish the process only took 10 business days. I hope this helps!
Something for the ato to consider: the wording on the ato website mentions that you cannot sign a contract until they have 'released' the amount to you. However, no where in the FHSSS portal is the actual word 'release' used, instead they use words such as received, transferred and payment. I found it difficult to interpret when there is no clear definition of what 'release' actually means, screenshots of what to look out for would have been helpful.