Transitioning from doing things offline to online editing with QField can be really straightforward if you already have a server and you don't have any special requirements.
You can create your QField portable project with PostGIS-layers as you would with filebased layers: the platform for set up is a QGIS project (qgz). Still, there are a couple of things to take into account:
With PostGIS-layers there are a lot of possible configurations to do in PostgreSQL. You might want a different user account for every person using a tablet or maybe one is enough. One can easily set up different restrictions and privileges. For example if no feature should be deleted in any case you could set up a restriction to prevent that. All your configurations in PostgreSQL will be in place in QField as well.
Once you're in QGIS, configure needed PostGIS-connections as you would normally. If you save connection password to your .qgz-file QField won't ask you for the password once working with tablet, otherwise you'll have to provide a password there as well. If you choose to save password to your project file please note that it will be transferred to your mobile devices inside a text file and that it is readable.
In QFieldSync-plugin choose no action option for all PostGIS-layers you wish to edit in QField. Then package your project as you would normally. The same portable project can be distributed to all devices.
Note that from here on out you'll have to have a reliable internet connection in the field.