Well, the thing is that the event that divided the Earth into two neat hemispherical pieces, and moved them apart by such a great distance has to be magical. Actual physical forces are never so precise, and involve a lot of free heat, which melts most of the various constituent pieces, and vaporizes a fair sized bit, as well.
The Moon was probably the result of a chunk of proto-planet about the size of mars which hit the Earth a glancing blow, and blasted off a great glowing glob of melted crust and mantle. That took at most a hundred million years to settle down into a single mass. The earth was round again long before that. Several things made the Moon take so long to collect. It was spread out a good bit by the force of the impact. The various orbital elements had to run out their changes as it all collected or was ejected from the system, or fell back to Earth. It was all very hot, even some of it vaporized, and had to cool off, as well as collect into a single mass.
Now, your two hemispheres are not vaporized, but they are extremely asymmetric, and only the outer one-percent of one side is truly solid. So, the core and lower mantle will flow fairly rapidly to a roughly spherical shape (ignoring ripples from sloshing about as it collapsed) about 3000 miles in radius. The thin shell of rock above will simply fall into the magma now hundreds of miles below it. Actually, it would fall right along with the flow of magma, and get tossed about in those ripples I mentioned.
(WAG warning, I didn’t do the math.) The system would be spherical within rough limits in a matter of weeks, or months from a distant perspective. Of course the resulting changes in geology are profound, since the area of tectonic plates is equal to half the surface area of the original Earth, but now covers an area eight million square miles greater than half the surface of the original Earth. That means eight million square miles of exposed Magma, and sloshing liquid rock, into which the seas have poured, and promptly evaporated. Weather is hardly the word to describe it. Cataclysmic geological events such as the many great extinction events pale in comparison.
Neither half planet has sufficient gravity to hold it’s current half of the available atmosphere, but outgassing from all that magma will be providing many new elements into the new atmospheres of each for thousands of years, perhaps millions. Volcanism takes on new meanings as well, in a planet with ten percent exposed mantle, and an asymmetric core. I can’t even begin to guess how the day would vary from our current one. Of course the year would be different for each of the halves, since their orbits have been magically altered to who can say what.
Not that there would be anyone to report all this. Everyone died in the original sloshing, where crustal movements of Richter Scale Values in the hundreds were hourly events for weeks at a time. (I point out that 8.7 is the historic record in our species experience, and 10 the maximum I have ever heard referred to from geological records.) Pyroclastic flows so numerous that they would have flow systems like hurricanes, only on scales larger than the largest hurricane ever imagined. (Imagine hurricane force winds of thousand degree ash and gasses colliding in whirlpools over thousand mile wave fronts.) After that, everything rebounds from hitting the waves coming the other way around the world.
But it would look round, from far away. It would be fairly round, too, in a hundred years or so, give or take a bulge or two, here and there.