问题是您向.day()传递了一个错误的参数，传递了一个从0到6的数字（或者是当天的全名，但我不确定这个替代方案的效果如何）。
下面我把一个更紧凑的函数和你正确的一个。

const fakeDay = 2; // 2 is Tuesday, change it for simulate a day sun: 0, mon: 1, tue: 2, wed: 3, thu: 4, fri: 5, sat: 6

function findNearestFreeSlot(slotsArray) {
  const currentDate = moment().day(fakeDay);
  let nearestDayDiff = Infinity;
  let nearestSlot = null;

  const indexDays = { sun: 0, mon: 1, tue: 2, wed: 3, thu: 4, fri: 5, sat: 6 }; // Add this index number: day

  for (const daySlots of slotsArray) {
    const { day, freeSlots } = daySlots;

    for (const slot of freeSlots) {
      const slotDateTime = moment(slot, 'h:mm a').day(indexDays[day]); // <---- use the index

      // Check if the slot is on or after the current date
      if (slotDateTime.isSameOrAfter(currentDate)) {
        const diffDays = Math.abs(currentDate.diff(slotDateTime, 'days'));

        if (diffDays < nearestDayDiff || (diffDays === nearestDayDiff && slotDateTime.isBefore(nearestSlot))) {
          nearestDayDiff = diffDays;
          nearestSlot = slotDateTime;
        }
      }
    }
  }

  return nearestSlot ? nearestSlot.format('ddd, h:mm a') : "wait for next week";
}

function findNearestFreeSlotMyTry(slotsArray) {
  const currentDate = moment().day(fakeDay);

  const indexDays = { sun: 0, mon: 1, tue: 2, wed: 3, thu: 4, fri: 5, sat: 6 };

  const listSlots = slotsArray
    .reduce((prev, { day, freeSlots }) => { // Converto the object of free slots in to array with the difference
      for (const slot of freeSlots) {
        const dateSlot = moment(slot, 'h:mm a').day(indexDays[day]);
        const diff = dateSlot.diff(currentDate);
        if (diff >= 0) prev.push({ diff, date: dateSlot.format('ddd, h:mm a') }); // Get elements only if is in the fucture
      }
      return prev;
    }, [])
    .sort((a, b) => a.diff < b.diff ? -1 : 1); //  sort the array by diff, from the nearlest to further

  return listSlots?.[0]?.date || 'wait for next week'; // Return the date or the string
}

const freeSlotsArray = [
  {
    day: 'wed',
    freeSlots: [/* '12:00 am', */ '12:00 pm', '1:00 pm', '1:30 pm', '2:30 pm', '3:00 pm', '3:30 pm', '4:30 pm', '5:00 pm', '6:30 pm', '7:00 pm']
  },
  {
    day: 'sat',
    freeSlots: ['7:00 am', '7:30 am', '8:00 am', '9:00 am', '10:00 am', '10:30 am', '11:30 am', '12:00 pm', '12:30 pm']
  },
  {
    day: 'thu',
    freeSlots: ['12:00 pm', '1:00 pm', '1:30 pm', '2:30 pm', '4:00 pm', '5:30 pm', '6:30 pm', '7:00 pm']
  },
  {
    day: 'mon',
    freeSlots: ['4:00 pm', '4:30 pm', '6:00 pm', '6:30 pm', '7:30 pm', '8:00 pm', '8:30 pm', '9:30 pm']
  }
];

const nearestFreeSlot = findNearestFreeSlot(freeSlotsArray);
console.log('-----> ', nearestFreeSlot);

const nearestFreeSlotMyTry = findNearestFreeSlotMyTry(freeSlotsArray);
console.log('-----> ', nearestFreeSlotMyTry);

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