As I understand from this IBM post both the IBM and Google teams have independently built 53-qubit processors. What is the significance of the number 53? It is purely coincidental, or is there a deeper reason why both team have the same number of qubits?
It's just a coincidence.
I can speak from personal recollection on the Google side. Google originally intended to use a 72 qubit chip (Bristlecone) where qubits were essentially directly connected to each other. They then switched to an architecture where qubits were connected indirectly via a coupler. The coupler requires a control line, so this increased the number of wires per qubit. The fridge was only setup for so many wires, so the total number of qubits was reduced to 54 to fit. Then one of the qubits didn't work, so it was excluded from the experiment leaving 53.
That being said, an underlying reason that you would expect slightly-more-than-50 qubits to be a common target is that that's roughly the number of qubits where the wavefunction becomes so large that it can't be directly stored on modern supercomputers.
My guess is that this is an example of co-opetition, i.e. collaborative competition. Number of qubits is just a single characteristic of a quantum processor, but there are a lot more, like tolerance, topology, etc. Also this characteristic is the only one that most people understand. Thus it's not reasonable to put all the resources on the increasing just this number (or use some shady marketing). It's better to be aligned and invest into the overall performance of a chip. Until a breakthrough, of course.
I'm sure that this has something to do with quantum decoherence or "noise" which is caused when more qubits are added. It's likely that they are both at the frontlines of research so 53 qubits are the best that they can do given the hardware that they have access to. As they add more qubits it gets tougher to compute and prompts them to find some suitable method to reduce this noise through quantum error correction.