Mostly on how much Processing power you have, commonly messured in FLOPS. Or Floating Point Operations / second. Making a Computer physically huge is usually the last thing you want to do for speed, because individual cycles are so short the signal physically cant travel very far.
A very rough example would be; Imagine a piece of Data on your Earth sized iMac is stored on the other side of the world, well now it is gonna take at least 1/3,5 or so of a second to get that bit of information. Since no matter what you try the speed of light is set.
At the scale of a Planet, this becomes a huge issue because varrious parts of the Computer have vastly differnt latency. Which computers really dont like. For example, the Traces on a Mainboard are all specific lengths and if they are not within the expected length down to i belive a micrometer (dont quote me) the whole Computer just kind of dosnt work.
Furthermore, i would have to question the precision of such an operation. Modern Computer parts are made on the nm scale. And i am just gonna doubt Nanits can do that. They cant. So it is likley the actualy density of transistors on your Planet wide computer will be very low with a lot of error in it. Error in this case means parts that dont work, bits that are to long or short etc. All of which means you have to aim for lower and lower performance. As the high performance CPU´s and GPU´s we have nowdays just dont work if you dont have the tolerances of Atoms.
These are just some of the limitations i can think of that will really prevent this from being to fast.
Another question is precisly what kind of Computer we are talking about. Prosumably it is not actually an iMac and i am just gonna guess the Planets surface is not covered in 4090´s. Since you allocate so little power to the whole thing (Powering a Computer 10km deep and 10000s of km² large with Geothermal is... an interesting proposal), i can only imagne what you are building is a low power, high redundancy system that is supposed to crunch the numbers on something for a hot minute. Which only makes sense if the scale of the system outweighs the downsides of its speed disadvantage.
Or in other words, is it easier to build a 10km wide sphere out of 1nm 9090´s that does 20 Octaflops and consumes the yearly power budget of a K1 Civilisation each second OR to transform a Planet into something that does 1 Octaflop but dosnt bankcrupt a K2 Civilisation ?
In any case, what might any of these be used for ? Well i would ask what the point of it in Story is but aside. Prosumably such a Computer would be used to takel problems that cannot be solved in a better way. Be that trying to unify General Relativity and Quantum Mechanics or break Thermodynamics. Maybe you want to simulate a lot of People or you really want to know what happend at the Big Bang.
The issue really is that any application is going to be very abstract and it is questionable if such a huge computer has any practical use. For example, such a Computer could probably Unify General Relativity and Quantum Mechanics. But will that be useful ? In that, because we have not been able to do it thus far, any potential solution is going to be so complex that it makes Quantum Mechanics and GR look like 1st Grade math problems. It is very likley that if such a theory exsists (Which keep in mind, it might just straight up not), its going to be very meaningless to Humans, i mean for most people this is pretty meaningless
And thats part of the easiest solution to General Relativity. Imagine how bad it gets when you merge QM and GR.
My point here is that if you seriously consider making a computer of that scale you might want to exhaust other possibilities first. As there is always the option that you are wrong, and that Computer will not find anything.