In new Contacts, group contacts with labels. However, as of December 2018, if a contact has multiple email addresses, you can't specify which email address to use when use that contact group in an email, for example. As a workaround, create a separate contact with only the email address you want to use in the label/group.

Create a Separate Contact and Add It to a Label/Group

1. Sign into Contacts at www.google.com/contacts
2. If you haven't already, create the label:
   1. In the list on the left under Labels, click Create label
      
   2. Type your label name and click OK, and you will see your new group in the list on the left
3. On the top left, click Create Contact
4. Fill in the contact fields, adding only the email address you'd like to use in the label/group and click Save
   
5. Click the three-dot button, and under Change labels, select the label you want to add