Dear Fridaleen,
Good day! Thank you for reaching out to the Microsoft Community. We're delighted to happy.
We've conducted a quick test, and we found that copy plan function is available for basic plans added to group and premium plans. However, it is missing from basic plans that are not added to a group.
For your reference: The new Microsoft Planner for the web is available in Targeted release! | Microsoft Community Hub

In this situation, if you are having concern with Basic plans not connected to a group that can be reproduced on our side, considering that the Product Team is continuously working on updates and improvements for Planner, and they frequently check customer comments and feedback, we highly recommend sharing your valuable feedback using the feedback button within Planner
or in the Planner Feedback Community. Please also vote for similar feature requests on the feedback site, such as:
Many features have been developed or improved based on user feedback. Your feedback and vote will increase the awareness coming from the related team. This is the quickest route to get your feedback to the developers’ ears.
If you are experiencing this issue with Basic plans added to a group or Premium plans, we recommend contacting your admin to check if the tenant is a target released tenant to see the new change. For admin reference: Set up the Standard or Targeted release options - Microsoft 365 admin | Microsoft Learn
If so, please switch to a different browser with InPrivate mode and test with different networks to check the outcome. If the issue persists, it might be related to a background service that needs to be checked from the backend. More resources may need to be involved to help further.
In this situation, we sincerely recommend contacting your Microsoft 365 administrator and following the steps in this article to create a support ticket with Online Support. The support team has higher permissions than we do and can remotely help check the situation on your side, involve more resources to collect logs, and help you troubleshoot. This would be a more efficient way to handle this case for you.
For reference: How do I find my Microsoft 365 admin?
If the understanding above is not consistent with yours, please feel free to post back and point that.
Sorry for the inconvenience again. Your patience and understanding are highly appreciated. Hope you stay safe and healthy.
Sincerely,
Rhoda | Microsoft Community Moderator