I recently purchased a Brazilian rain tree from a local nursery. It is pre-bonsai. I don't know the best way to explain the situation, but I will try. The tree feels "loose" in the soil and the tree wobbles. Because this is a new tree, and it is winter I do not want to repot. I am wondering, would it be better to wait until spring/summer to repot or should I just add some soil to the current pot? Or is it not a big deal? I was hoping to wait until spring/summer of 2023 to repot. I can try to upload pictures/videos tomorrow.

It could be that is has rooted only on one side, and that transport loosened the soil a little.

I would repot in spring.

Bonsai is repotted when it is root bound. A wobbly tree is not root bound. Hence do not need repotting. It needs to be fixed to the pot. Roots will grow and stabilice the tree.

You can guy wire it to the pot, to help roots to develop.

it is possible to have a photo of the tree

Albas wrote:

You can guy wire it to the pot, to help roots to develop.

That is what I would do.
Usually I use a natural piece of string that will last three months, enough for the roots to be well attached to the ground.