Inductance Calculation for the ST25DV04K DISCO Kit Flex Antenna
When I extracted the dimensions from the Gerber files of the flex antenna included in the ST25DV04K DISCO kit and entered them into your online tool, the calculated inductance was 5.69 µH. The input capacitance of your IC is 28.5 pF.
Using the resonance frequency formula and substituting (L=5.69,\mu H) and (C=28.5,pF), the calculated resonant frequency is approximately 12.5 MHz, which is below the target frequency of 13.56 MHz.
I also noticed that the PCB layout includes a footprint for an additional parallel capacitor, presumably for tuning the antenna. Adding a capacitor in parallel would increase the total capacitance and further lower the resonant frequency.
Could the inductance value calculated by your online tool be inaccurate? I have attached a screenshot showing the parameters I entered into the tool for reference.

