- predecessor is erased, both resulting individuals are new - too dark for something like this, so most likely no.
- both are a copy of the original, this implies that the original ceases to exist, so let's consider the functionally identical option of the original splitting off half of their mass to create a perfect copy of themselves, including memories and personality - could definitely be used at some point in this manga as setup for a threesome (or more), that is given that they can later all merge back into one.
- both splits contain part of the original's consciousness, with it being shared between them - same as above point.
- original splits off a part of her mass to create a completely separate, new individual (basically a slime baby) - i feel like this is also extremely likely in this scenario, as otherwise all slimes would simply be copies of the original first slime, including memories since then, meaning they'd all effectively be extremely old (as old as their species) and behave much differently to what we see here. this also opens the path up to eventual "slime daughter" arc if this goes far enough.
in short: i believe it's likely to be a combination of the last 3 points, with the last one (the slime baby) likely being the main method, and the other 2 mostly being a novelty gimmick that isn't really used in a permanent manner, but rather with the intent of the copies eventually merging back into a single individual at some later point in time.