Here is one way you can accomplish this using reduce()

let tasks = [{
    id: 1,
    title: "call Tom",
    reminders: {
        date: "2022-02-01",
        time: "09:30"
    }
}, {
    id: 2,
    title: "Meet Bred",
    reminders: {
        date: "2022-02-01",
        time: "10:30"
    }
}, {
    id: 3,
    title: "Mail Susan",
    reminders: {
        date: "2022-03-01",
        time: "19:00"
    }
}];

let combinedTasks = tasks.reduce((combined, x) => {
    // Try to find an existing item in the combined tasks array where the date equals this task item.
    let match = combined.find(y => y.reminders.date == x.reminders.date);
    if (match) {
        // If we find a match, add this task item's title to the combined item's tasks array.
        match.tasks.push(x.title);
    } else {
        // If we didn't find a match, take this task item and turn it into a combined tasks item with a tasks array so that future items in the tasks array can be combined with this one.
        let copy = { ...x };
        copy.tasks = [x.title];
        delete copy.title;
        combined.push(copy);
    }
    return combined;
}, []);


console.log(combinedTasks);

const tasks = [
{
 id: 1,
 title: "call Tom",
 reminders: {
  date: "2022-02-01",
  time: "09:30"
 }
},
{
 id: 2,
 title: "Meet Bred",
 reminders: {
  date: "2022-02-01",
  time: "10:30"
 }
},
{
 id: 3,
 title: "Mail Susan",
 reminders: {
  date: "2022-03-01",
  time: "19:00"
 }
}
]
tasks.sort((a,b)=>{
  return new Date(a.reminders.date) - new Date(b.reminders.date)
})

let output = [];
tasks.map((val,index)=>{
   if(index===0){
      let obj = {}
      temp = [];
      temp.push(val.title);
      obj.id = val.id;
      obj.tasks = [...temp];
      obj.reminders = {...val.reminders};
      output.push(obj);
   }else{
      if(output[output.length-1].reminders.date===val.reminders.date){
         output[output.length-1].tasks.push(val.title);
      }else{
          let obj = {}
          temp = [];
          temp.push(val.title);
          obj.id = val.id;
          obj.tasks = [...temp];
          obj.reminders = val.reminders;
          output.push(obj);
      }
   }
})

Try this solution , it works .

Output : 
[
  {
    id: 1,
    tasks: [ 'call Tom', 'Meet Bred' ],
    reminders: { date: '2022-02-01', time: '09:30' }
  },
  {
    id: 3,
    tasks: [ 'Mail Susan' ],
    reminders: { date: '2022-03-01', time: '19:00' }
  }
]

Output of this code is as expected . I hope this is helpful .

you are right, you have to use the reduce method.

Use it to loop over your initial array. So for each task, you can watch in your futur array if you have a task at the current task date. Else you can create a new task and add next tasks later.

const tasks = [
    {
        id: 1,
        title: "call Tom",
        reminders: {
            date: "2022-02-01",
            time: "09:30"
        }
    },
    {
        id: 2,
        title: "Meet Bred",
        reminders: {
            date: "2022-02-01",
            time: "10:30"
        }
    },
    {
        id: 3,
        title: "Mail Susan",
        reminders: {
            date: "2022-03-01",
            time: "19:00"
        }
    }
];

const combinatedTasks = tasks.reduce((_combinatedTasks, currentTask) => {
    const currentDate = currentTask.reminders.date;
    const combinatedTaskAtCurrentDate = _combinatedTasks.find(task => task.reminders.date === currentDate);
    if (combinatedTaskAtCurrentDate) {
        combinatedTaskAtCurrentDate.tasks.push(currentTask.title);
    } else {
        _combinatedTasks.push({
            id: currentTask.id,
            tasks: [currentTask.title],
            reminders: currentTask.reminders
        });
    }
    return _combinatedTasks;
}, []);

console.log(combinatedTasks);