I am aware that sky pier and ferry service are open for SZ to HK at the moment, but not sure about the exact procedures and eligible airlines. The part of "upstream check in services" from the HK airport announcement confuses me a bit, since i have never used the pier before and I have no idea what is what there.
link to the announcement: https://www.hongkongairport.com/en/transport/mainland-connection/ferry-transfer.page
According to the page you link, only the ferry from Shenzhen Shekou Port to Hong Kong Airport is currently running. So, consult the list of participating airlines and make sure your airline has a checkmark in the Shenzhen Shekou Port column.
(Under ordinary circumstances, it is sometimes possible to take the ferry and then check in at the airport if you are flying with a non-participating airline, but it seems this service is suspended during the current covid-19 situation.)
Note that the ferry schedule is currently quite limited, so you will want to ensure that there is a ferry available which will get you to the airport at the appropriate time and that your airline is permitted; otherwise, you will have to find another way to travel to the airport.
