The cohabitation evidence is to show you lived TOGETHER in the same house for the last 2 years... so if you are applying in January you need to show you lived together from January 2020 to January 2022.
You need 1 official document dated every 4 months, addressed to both of you at the same address... either a joint document or 2 individual ones and they must have been received in the post (though for an AirBnB you may need to use an online document if there were no paper documents given to you).
So, you will need evidence from:
Jan 2020
May 2020
Sept 2020
Jan 2021
May 2021
Sept 2021
Jan 2022
From what you've said:
Jan 2020 - you should have evidence of living together in the UK
May 2020 - you should have evidence of living together in Australia (AirBnB)
Sept 2020 - she was in the US, so you won't be able to provide evidence of living together
Jan 2021 - she was in the US, so you won't be able to provide evidence of living together
May 2021 - she was in the US, so you won't be able to provide evidence of living together
Sept 2021 - you should have evidence of living together in the UK
Jan 2022 - you should have evidence of living together in the UK
They can make some exceptions for not living together for the entire 2 years if you have a very good reason for why this was not possible... normally, good reasons would be things like military deployments or being sent abroad for work by your UK company and your spouse having to stay in the UK, but I would hope they would accept Covid travel restrictions as good reasons.
You would need to write a letter explaining the situation, and also provide evidence of your relationship subsisting during the entire time she was in the US between August 2020 and June 2021, so you would need to include things like letters, cards, emails, messages showing regular communication between you (like you did for the initial visa in 2019).