Considering you have only had Bmo for 13 days, it's truly wonderful the progress you have made in such a short amount of time for your Bmo to already be so trusting of you and your family. In fact it's remarkable that he has mastered the step up command and is spending out of cage time with you.
The behaviours you have described are also normal especially for a new bird who is in the process of getting used to a new home.
Soon enough your Bmo will start to show interest in his toys.
If you set up a little play area for him when having out of cage time, you can even encourage him to play with a toy or two. The singing and more playful activity will also soon be followed. You will have a better idea on your Bmo's personality by watching and continuing to interact with him for the next couple of months.
From your description, it seems Bmo has the real potential of being a great friend and companion to you and your family and to be perfectly happy happy as a solo budgie.
For now it would be best to focus on strengthening the bond you have with Bmo and in a few month's time if you feel that according to your budgie's personally and for his overall happiness and well being he would benefit more from the companionship from a same species friend, then you can get him one.
You may find the info on this link useful: https://talkbudgies.com/articles-gene...en-flocks.html