It's great that actions will be undertaken on threads rather than whole messages.

When a conversation is moved to a folder, will it move all items irrespective of folder or will it leave the sent messages in sent folder and just reference them in the folder as part of the thread?

Good point.
The operation will indeed only apply to the mails in the same folder, which is probably not what we want when moving to trash, but is probably what we want when we move to another folder....

What technically happens is that we list mails in a folder, and "merge" (reduce) them by threadid. We then simply collect all id's that were merged that way, and on any modification apply the modification to all the merged mails.

But then delete should move all messages in same folder in the thread to trash

I think operations should be carried out across the thread fully, such that when:

1. When a conversation is over to trash - the whole conversation is done so.
2. When a message is moved to a folder, all components of the thread are done too.

But this is my opinion only. So far what is proposed is what is done in Apple Mail (flags on conversation rather than emails). Apple Mail also only moves emails to thread not in sent folder.

But I guess you'll have to take into consideration what Roundcube Next does too, such that there is consistency across the desktop client and web interface to avoid confusion for users.