Payments vary depending on what state you live in.For most an...

Payments vary depending on what state you live in.
For most an eligible recipient is someone already getting payments or have a specific type of concession card as listed on the Federal site.
https://www.energy.gov.au/energy-bill-relief-fund/energy-bill-relief-fund-households

The WA state Government generously gave every household a rebate.

For Vic the next part payment is due next year.
https://www.energy.vic.gov.au/households/help-paying-your-bills
has schedules for various types of eligible households.

For example:
Existing concessions recipients
First instalment
If you already receive a concession, your energy retailer will automatically apply the first instalment of $125 to your account in August 2023; you do not need to provide any further information. You should receive this payment on your electricity bill from September 2023 onwards.
Second instalment
A second and final instalment of $125 will be applied to your account in February 2024. You should receive this payment on your electricity bill from March 2024 onwards.