The Raspberry Pi camera with teh lens space gives a field of view similar to a 20x objective (see Comparison of a pi-camera and a 20x optical lens - Contributions - OpenFlexure Forum)
This means that the shift that you are seeing is quite large compared to the expected drift of the static stage from the paper that I linked earlier. However as you are also moving to different parts of the slide I would expect the repositioning to have larger changes than the static drift.
Image processing is not my core expertise, but what you are needing is basically to search for the position of a small image within a larger one. Fiji probably can do this. I am imagining that you centre the microscope field of view on the interesting features for the first set of pictures for the first time step. You can then cut out the central portion of that first image as the part you are actually going to use. On the second time step you look in the new picture for the area of the new picture that looks the most similar to the first picture. You can then cut out that area to be the second picture that you use, and so on. The detail of the method will be how much it moves, so how tightly you need to crop the image to make sure there region is present in all images. Then whether there is enough in the image that is the same throughout your timelapse that you can do the matching. You may need to have deliberate markers that you can search for if your specimen is changing a lot.