The DatePicker Limits are applied to the app when 'Limits' option under the Inspector Window are changed. All the dates beyond these limits automatically get disabled once the Limits are set. The range appears to be between 2002 and 2042 since when the app is run, the default datetime value is the current date. Since the app is running in the year 2022, MATLAB shows a list of years lying within the range of +/- 20 years. However, once the date gets changed to say 2002, the range will shift to 1982-2022. The dates which are beyond the limts set earlier will automatically get disabled and cannot be chosen.
Hope this helps!