I believe that there are two approaches: 1) repeat the binarization step that led to these images that you have right now; 2) consider various options based on image size. Let's focus on the second approach asked by the question.
Only two digits are connected in your smallest image, and this only happens when considering 8-connections. If you process the image as 4-connected, then there is nothing to do, because there are no two connected components that must be separated. This is shown below. The correct image can be obtained simply by finding points that are connected with another, only when considering 8-connectedness. In this case, there are only two such points, and deleting them, we turn off the two digits "1".


In another image, this is no longer the case. And I don’t have a simple application method on it that can be applied on a smaller image without making it worse. But, in fact, we could consider scaling both images to some common size using the nearest neighbor interpolation so that we don't go from the binary representation. By resizing both images so that they are 200 and keep the aspect ratio, we can apply both morphological methods to them. First do thinning:

Now, as you can see, the morphological branch points are the ones that connect your numbers (there is another six, which will be processed). We can extract these branch points and apply a morphological closure with a vertical line of 2 * height + 1 (the height from your image), so no matter where the point is, closing it will lead to a full vertical line. Since your image is not so small, this line should not be 1 point-wide, in fact I considered a line 6 pixels wide. Since some branch points are horizontal, this closing operation will connect to them in the same vertical line. If the branch point is not close to another, then erosion will remove the vertical line. And by doing this, we remove the branch point associated with the number six on the left. After applying these steps, we will get the following image on the left. Subtracting the original image from it, we get the image on the right.


If we apply the same steps to the “8011” image, we will end up with exactly the same image that we started with. But this is still good, because, using a simple method that removes points that are only connected with 8-connectedness, we get the separated components, as before.