After the transfer of ownership is completed, you will need to change the billing account too, in order to link it to the billing account of the new user
On new Owner's account, go to Billing in the "hamburger" menu and either link the project to an existing billing account or set up a new Billing account to link the project to.
On the new Owner's account, go back to the IAM section and delete your account from the list by clicking the pencil on the right and then the trash can icon.
PencilTrash can