First, check date not in disabledDates before setDate to datepicker.
Simply check date not in disabledDates by format date to string format 'yyyy-mm-dd' (https://stackoverflow.com/a/3552493/9002484) and use include funtion to check like this.
dtf = new Intl.DateTimeFormat('en', { year: 'numeric', month: '2-digit', day: '2-digit' }) 
let [{ value: mo },,{ value: da },,{ value: ye }] = dtf.formatToParts(date)
let formatedDate = `${ye}-${mo}-${da}`
if(!disabledDates.includes(formatedDate)){
// not include in disabledDates; so assign date
}else{
// include in disabledDates; do nothing
}
then loop until the selected date not include in disabledDates 
$('.next-day').on("click", function() {
   var date = $('#picker').datepicker('getDate');
   while (true) {
     date.setTime(date.getTime() + (1000 * 60 * 60 * 24))
     dtf = new Intl.DateTimeFormat('en', {
       year: 'numeric',
       month: '2-digit',
       day: '2-digit'
     })
     let [{
       value: mo
     }, , {
       value: da
     }, , {
       value: ye
     }] = dtf.formatToParts(date)
     let formatedDate = `${ye}-${mo}-${da}`
     if (!disabledDates.includes(formatedDate)) {
       break;
     }
   }
   $('#picker').datepicker("setDate", date);
 });
You can make function that find next date that not in disabledDates and the code will be like this.
function findNextDateBySkipedDate(startDate, operation, skipedDates) {
   let date = new Date(startDate.getTime()); // copy date to new object
   while (true) {
     if (operation === "+") {
       date.setTime(date.getTime() + (1000 * 60 * 60 * 24))
     } else if (operation === "-") {
       date.setTime(date.getTime() - (1000 * 60 * 60 * 24))
     } else {
       break;
     }
     dtf = new Intl.DateTimeFormat('en', {
       year: 'numeric',
       month: '2-digit',
       day: '2-digit'
     })
     let [{
       value: mo
     }, , {
       value: da
     }, , {
       value: ye
     }] = dtf.formatToParts(date)
     let formatedDate = `${ye}-${mo}-${da}`
     if (!skipedDates.includes(formatedDate)) {
       break;
     }
   }
   return date;
 }
 $('.next-day').on("click", function() {
   var date = $('#picker').datepicker('getDate');
   $('#picker').datepicker("setDate", findNextDateBySkipedDate(date, "+", disabledDates));
 });
 $('.prev-day').on("click", function() {
   var date = $('#picker').datepicker('getDate');
   $('#picker').datepicker("setDate", findNextDateBySkipedDate(date, "-", disabledDates));
 });