Is it possible somehow to identify the problem with the battery that evoked the message to replace the battery?
Not really. Why? What you see there is a point in time measurement of your battery. You’d need a lab with a bunch of diagnostic equipment.
Think of it like the gas gauge in your car. It will only tell you at that moment how much fuel you have in your tank. Now, if you were to place a large brick inside your tank, the gauge will still be reporting accurately, but it would have no idea that the capacity would have changed by exactly the volume of the brick.
To accurately identify the problem, you you'd need to measure a number of things like how much fuel you used to fill it, how much you consumed over a period of time etc. The number of fill ups you made would be irrelevant.
Same for your battery. It’s not a single battery cell that we fill with angry pixies each time we charge it. It’s actually a series of cells and if, while discharging, it runs into a dead cell (meaning no charge in it), all of the point in time measurements will drastically change “setting off alarms” that you may have a bad battery.
It’s important to remember that when measuring voltage, it looks at the aggregate amount. If it runs across a dead cell, the aggregate voltage will change, but so will the charge capacity and available current.
Why does it do this?
There’s a good chance your battery is bad or in the process of going bad. The number of cycles is only a “rule of thumb” and not a hard and fast number. Batteries can die with 100 cycles and they can continue to function well after 1000 cycles. The bottom line is that they are man-made devices and not without manufacturing defects. While rare, they do happen.
So, can you determine the exact cause of a failing battery? If you had the time and resources, yes. However, the cost prohibitive nature of this means it’s much, much, more effective snd efficient to just replace it.