I am trying to use a drawing tablet with Gimp. But it appears each tool has a different setting for mouse and tablet, so say if you adjusted the brush size for the tablet it's not changed for the mouse. Is there some way to change the tool settings for both mouse and tablet, so that it's possible to use both of them without hassle while working on an image.
Not what I see in 2.8 or 2.10. Tools options are the same for a given tool whatever the input device (ie, the brush is the same size, between mouse and tablet).
However, the brush may not be the same shape/size between two different tools (brush and pencil, for instance), and you can have different tools associated to mouse and tablet. You can ask Gimp to share tool options between paint tools, see
Edit>Preferences>Tool options>Paint options shared between tools