You have to mock the method as true, through component inheritance.

The constructor is called, on the line fixture = TestBed.createComponent(TestingComponent);, so the spyOn, is too late, which might be the issue.

You can simply convert the subject to a BehaviourSubject, through inheritance and just for testing this one particular scenario.

After doing this test case, you can continue using AppComponent, Since subject is not possible to subscribe when the code is in the constructor.

Also one thing to note, is that the afterNextRender will execute immediately when working on a non SSR context. Hence you are facing so many difficulties.

Spec TS:

import {
  TestBed,
  ComponentFixture,
  waitForAsync,
  fakeAsync,
  flush,
} from '@angular/core/testing';
import { AppComponent } from './app.component';
import { AppModule } from './app.module';
import { BehaviorSubject, firstValueFrom } from 'rxjs';
import { Component, input } from '@angular/core';

@Component({
  // ... // <- values similar to your component
  selector: 'my-app',
  template: '',
})
export class AppComponentTesting extends AppComponent {
  isDisabled: any = input(true);
  myStream = new BehaviorSubject(null);
  constructor() {
    // ... // <- same values as YourComponent.
    super(); // <- add args if needed. But your properties must be protected and not private.
  }
}

describe('AppComponent', () => {
  let component: AppComponent;
  let fixture: ComponentFixture<AppComponent>;
  let output;

  beforeEach(() => {
    TestBed.configureTestingModule({
      imports: [AppModule],
      declarations: [AppComponentTesting],
    }).compileComponents();
  });

  // in unit test
  it('should call the function when disabled is true', fakeAsync(() => {
    const fixture: ComponentFixture<AppComponentTesting> =
      TestBed.createComponent(AppComponentTesting);
    const component: AppComponentTesting = fixture.componentInstance;
    fixture.componentRef.setInput('disabled', true);
    spyOn(component.myStream, 'next');
    fixture.detectChanges();
    flush();
    expect(component.myStream.value).toEqual('hello');
  }));
});

TS:

import { Component, afterNextRender, input } from '@angular/core';
import { Subject } from 'rxjs';

@Component({
  selector: 'my-app',
  templateUrl: './app.component.html',
})
export class AppComponent {
  disabled = input(true);
  myStream = new Subject();
  constructor() {
    afterNextRender({
      write: () => {
        console.log('qwer', this.disabled());
        if (this.disabled()) {
          console.log('qwer1', this.disabled());
          this.myStream.next('hello');
        }
      },
    });
  }
}

Stackblitz Demo