Hello,
I used the trace bitmap function on inkscape and after modifying it, I removed the solid color background. I am wondering what function I use to add a background back to the traced image but having the background just be used inside of the image so no white square is shown? I usually just use the pen and trace the outline and then add a fill but I would imagine there is a function? Thanks in advance!

Well if you use Path menu > Trace Bitmap, there should be no need to trace the outline with the Pen tool. If I understand correctly what you're describing, you can just Ungroup the result from Trace Bitmap, and use the outline from the trace result. The rectangular background will be a separate object from everything else. After ungrouping, you could just delete the rectangle, and change the fill color of the other shape.

Yes, adding a fill color is the correct way to do it!