It looks like everybody else calls these linear resonant actuators, not accelerators. Once I figured out the terminology difference, it was much easier to find more information about their applications.
It did take a bit to understand what the actual subject was, it is quite interesting. I can visualize at least one way to track the actual resonant frequency, I am sure that there are a few more. The simplest way is to use the device in the feedback loop of it's driving oscillator, like the tuning fork oscillators used in the past. That would be the cheap and easy approach and it would not need a microcontroller or any software to make it work. So probably nobody would want to do it that way.
Good intro article. I have tried your DRV2603 LRA driver and it works very well. I would be interested in a follow up article that goes into detail about how auto-tune resonant frequency detection works.