[giomasce]

Suppose I want to do this with my laptop, and dump my drive to the cloud (say accessible via SSH) to reinstall another operating system overwriting it. It's likely that the new operating system won't touch most of the blocks in my drive, so when restoring after having passed the boundary I don't want to transfer those unchanged blocks. Is there a good tool to do that easily?

[BrandoElFollito]

If you use a SSD or above, you do not have any control over these "blocks" (called cells in these technologies). You cannot access them at all once they are unliked (i.e. the slack source you had with HDD which you could access does not exist anymore).