If white holes are just time-reversed black holes, then can they split just not merge? I have read this question:

Equations of fundamental physics are usually time-reversible (particle physics is time-reversible in a CP or CPT sense, though) which means you can take a certain reversal of the solution of your equations to obtain another solution. A white hole is a complementary object to a black hole in this sense. Every particle in it's field behaves the same as a particle near a black hole only with a reversed arrow of time.

White Hole Formation and Queries
And this one:

Thermodynamics forbids the splitting of a black hole in multiple smaller black holes. Reason being that the result of such a splitting would violate the first law of thermodynamics (energy conservation) and/or the second law of thermodynamics (entropy non-decrease).

Is there a way to split a black hole?
So basically, black holes do merge, we have experimental evidence for that, but on this site it is said that they cannot split. Does this mean that white holes can (because they are time reversed black holes) only split but cannot merge?
Question:

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*If white holes are just time reversed black holes, then can they split just not merge?

 A: The broken-egg thought experiment tells us that time reversibility is limited to basic, fundamental processes. The fusion of two black holes does not seem to be a fundamental process in this sense. I am not sure that your assumption is true that white holes are just time reversed black holes - there is no ordinary notion of time inside of the event horizon of black holes, and the entropy near the event horizon of black holes should be high, near white holes it should be very low (even the big bang could reveal to be a sort of white hole).
A: In classical black holes, there's a time asymmetry: the event horizon can be crossed from outside to inside only, while if you reverse the arrow of time then it can be crossed from inside to outside only. White holes are by definition black holes with the arrow of time reversed. The proof that black holes can merge but not split also proves that white holes can split but not merge, and all other time-asymmetric properties of black holes are also reversed in white holes.
In quantum gravity, it should be possible for a black hole to split by emitting a black hole as Hawking radiation, though it's vanishingly unlikely (as unlikely as any other process involving a similar decrease in entropy). It's not clear that quantum black holes have any properties that are asymmetric in time for any reason other than ordinary thermodynamic irreversibility. You can still consider a black hole that is time-reversed in the same sense that a positron is a time-reversed electron, but positrons don't have a reversed thermodynamic arrow of time, and there's no obvious reason why quantum black holes would have one either. So there may be no distinction between black and white holes in quantum gravity.
