Since the owner of the site will be the one paying the premium, the domain AND also setting up the payment information, I usually recommend setting up the client to be owner of the site. Helps so that you don’t need their banking or payment details as that can be sensitive to have their information on your account.
To be able to keep working on the site, you can be co-owner or website manager so that you can access and edit the site and the backend/dashboard of the site. If you are a contributor of the site, you will see it on your dashboard like normal.
As for the payment access, the payment manager can access payment options and settings so if the client wants to allow others to help with payments. Depending on the payment used on the site, this might work for them.