Hey there @stopwatcher, I'm seeing that there are a lot of items in your house still. Pets and plant pots also need to be removed. An easy way to do this is to go to the Game tab and click Housing > Clear House Parts, and you can clear each room. Edit: Also important to mention, your pets have to be not on a hoard and fully rested in order to be removable.

Once you've done this, go to Housing again and click My Houses, click the new house that you bought, and click Move Into This House.

Let me know how it goes!