I do not think it is coming to the current interface. If you want to copy more than a handful of messages, use the old classic interface (
https://classic.fastmail.com). in a new browser tab.
If you just want to copy one or two messages, here is a sick hack:
- Open the message you want to copy
- In he More menu, choose Redirect copy and the email address <your-user>+<folder>@<fastmail.tld>