It appears from your description it is working exactly as you have designed it. But that's not what you want.
You have it set to match Any of those criteria.
So, since Every Message matches every message, it will move every message regardless of the date.
Rules only work automatically on the Inbox when they arrive. It doesn't automatically process messages that are sitting in the inbox.
You will never receive a message that is older than 7 days, so that never trips.
Sent messages are not in the Inbox, so it will never trigger on the Date Sent.
When you run it manually, it will move every message because you told it to match every message.
Get rid of the Every Message criteria and you can then run that manually on both the Inbox and Sent Box.