This is not related to Gmail labels.
To “move” an email to a label in Gmail, use the move email action.
See also:
Tracking what happened with a processed email
Handling and notifying errors
Applying labels to an email is used to quickly see in the email list what happened with a processed email. Once a label is applied, if you double clicking on the email source, the list of emails shows the labels under the subject:
This action is typically used after a filter or a bifurcation action to apply different labels depending on the type of email we process:
