That’s what I mean with the migration.
That’s exactly right. Kirby automatically generates UUIDs for every newly created page and file. These UUIDs will then be uploaded back to server A together with your changed and added content.
Because the length and character set of the UUIDs is quite large and the source for random data is the best that PHP offers, the collision probability is so low that collisions throughout dozens of years of normal use of Kirby are not to be expected. That’s independent from whether you use one or multiple servers.