We do not have option 'To Copy to new/existing Ticket' for 'Portal Interaction' (as we have for Ticket's Email
Interaction) .Hope this answer your query on current behavior and this post can be set as 'Answered'.
Thanks and Regards,
While it is not possible to copy one ticket to another, you could do one of the 3 actions listed below.
1. From the ticket OWL, you can select the ticket and then group it under another existing ticket.
2. From the ticket detailed view, in the Sub-Tickets facet, you can link it to an existing ticket or link it to a new ticket as a sub ticket.
3. From the ticket detailed view, in the Related Items facet, you can create a new ticket from the existing ticket as a follow-up item.
Hope this helps.