How do I add values ​from an array to a form?

Since you have set the value of the options of the select to be id field

...
<mat-option [value]="contact.id">{{ contact.name }}</mat-option>
...

We must also patchValue the ids as an array, for this we use the javascript map operator, to fetch only the ids from the array of objects!

...
if (this.data?.task) {
  this.taskForm.setValue({
    assignedTo: this.data.task.contacts.map((x) => x.id),
  });
}
...

FULL CODE:

TS

import { Component } from '@angular/core';
import { CommonModule } from '@angular/common';
import { Inject, Optional } from '@angular/core';
import { MatButtonModule } from '@angular/material/button';
import { MatCheckbox } from '@angular/material/checkbox';
import {
  MatError,
  MatFormField,
  MatFormFieldModule,
  MatLabel,
} from '@angular/material/form-field';
import {
  FormControl,
  FormGroup,
  ReactiveFormsModule,
  Validators,
} from '@angular/forms';
import { MatDatepickerModule } from '@angular/material/datepicker';
import { MatInputModule } from '@angular/material/input';
import { MatOption, provideNativeDateAdapter } from '@angular/material/core';
import { MatButtonToggleModule } from '@angular/material/button-toggle';
import { TitleCasePipe } from '@angular/common';
import { MatSelect } from '@angular/material/select';
import { MatIconModule } from '@angular/material/icon';
import { MatRadioButton, MatRadioGroup } from '@angular/material/radio';
import {
  MAT_DIALOG_DATA,
  MatDialog,
  MatDialogModule,
  MatDialogRef,
} from '@angular/material/dialog';
import { Task } from '../../app/task';

@Component({
  selector: 'app-task-form',
  standalone: true,
  imports: [
    CommonModule,
    MatButtonModule,
    MatCheckbox,
    MatError,
    MatFormField,
    MatLabel,
    ReactiveFormsModule,
    MatDatepickerModule,
    MatInputModule,
    MatFormFieldModule,
    MatButtonToggleModule,
    TitleCasePipe,
    MatSelect,
    MatOption,
    MatRadioGroup,
    MatRadioButton,
    MatDialogModule,
    MatIconModule,
  ],
  templateUrl: './task-form.component.html',
  styleUrl: './task-form.component.css',
})
export class TaskFormComponent {
  protected readonly Object = Object;
  taskForm!: FormGroup;
  fromPopup = false;

  constructor(
    @Optional()
    @Inject(MAT_DIALOG_DATA)
    public data: { fromPopup: boolean; task: Task }
  ) {}

  ngOnInit() {
    this.fromPopup = !!this.data?.fromPopup;
    this.taskForm = new FormGroup({
      assignedTo: new FormControl(''),
    });

    if (this.data?.task) {
      this.taskForm.setValue({
        assignedTo: this.data.task.contacts.map((x) => x.id),
      });
    }
  }

  public onSubmit() {
    console.log('Submitted');
  }
}

HTML

<div>
  <div>
    <div mat-dialog-title>Edit Task</div>
  </div>

  <mat-dialog-content>
    <form [formGroup]="taskForm" (ngSubmit)="onSubmit()">
      <mat-form-field>
        <mat-label>Assigned to</mat-label>
        <mat-icon color="primary" matSuffix>group_add</mat-icon>
        <mat-select formControlName="assignedTo" multiple>
          @for (contact of this.data.task.contacts; track contact.id) {
          <mat-option [value]="contact.id">{{ contact.name }}</mat-option>
          }
        </mat-select>
      </mat-form-field>
    </form>
  </mat-dialog-content>

  <mat-dialog-actions>
    <button mat-raised-button color="primary" type="submit">
      {{ data?.task ? 'Update Task' : 'Create Task' }}
    </button>
    <button mat-raised-button mat-dialog-close type="button" color="warn">
      Close
    </button>
  </mat-dialog-actions>
</div>

PARENT:

import { Component } from '@angular/core';
import { bootstrapApplication } from '@angular/platform-browser';
import { TaskFormComponent } from './app/task-form/task-form.component';
import { filter } from 'rxjs';
import 'zone.js';
import { MatDialog } from '@angular/material/dialog';
import { Task } from './app/task';
import { provideAnimations } from '@angular/platform-browser/animations';

@Component({
  selector: 'app-root',
  standalone: true,
  imports: [TaskFormComponent],
  template: `
    <button (click)="editTask()">Edit Task</button>
  `,
})
export class App {
  name = 'Angular';

  constructor(private dialog: MatDialog) {}

  public editTask() {
    let task: Task = {
      id: 1,
      contacts: [
        {
          id: 1,
          name: 'John Doe',
        },
        {
          id: 2,
          name: 'Jane Doe',
        },
      ],
    };
    this.dialog
      .open(TaskFormComponent, {
        data: { fromPopup: true, task: task },
      })
      .afterClosed()
      .pipe(filter((task) => task))
      .subscribe((task) => {
        console.log('Edit Task');
      });
  }
}

bootstrapApplication(App, {
  providers: [provideAnimations()],
}).catch((err) => console.error(err));

Stackblitz Demo