Generally speaking, computing is easier when working in base two. I can't speak for this computer or quantum computing specifically, but for parallel computing, pretty much every algorithm is simpler to implement on a base 2 number of processors. Not that it can't be done in non base two, just that base two eliminates tons of edge cases. I'd guess something similar is being done here too.

The most likely reason is that it gives an easy analogy between classical computing and quantum. The types of problems quantum are supposed to separate themselves with involve a lot of iterative steps for classical computers.

The output of classical computers can be larger than the number of bits that the processor works with. For instance, in some mathematics software you can do math with numbers much bigger than 2^64. Quantum computers can’t really do that. They have to fit each step of the problem into their bits at the same time to process. In essence, you can only solve problems that will output how ever many qbits you have, or less.

In fact, quantum computers must interface with classical computers to set the inputs and read the outputs. This requirement for interfacing with classical computers means that using a power of two makes some sense.

Finally, qubits represent a binary state, so the data representation is analogous to binary. The resulting qubits will always represent a 0 or a 1. For most computer scientists, it makes sense to conceptualize binary results in base 2.

These reasons are not important or required.

If you look at Google and IBM superconducting quantum processors, they don't use this base 2 for quantum processors (Google's paper on quantum supremacy for instance had 53 qubits and the new IBM one claim to have is 127). It might be due to this architecture with atoms instead of superconducting circuits, but on theory there is no need for base 2.

The Quantim Processing Unit is built on top of basic entities called QuBits. This is a physical realization of the quantum equivalent of a bit. However unlike a bit which can only take one or the other state (0 or 1) the QuBit can exist simultaneously in both states. The QuBits are on an atomic level electrons (the type of their spin are their states) or photons (their type of polarization are the states). TLDR: QuBits can take a continuous range of states and is not limited by the power of 2

I could be wrong. This is based on my very limited understanding of quantum computing.

https://en.m.wikipedia.org/wiki/Qubit

In general they are not. There are plenty with numbers of qubits that are not a power of 2. Especially because when building one, not everything will be perfect and it can happen that you can't use a few of the Qubits.