How to show that the last mat-step is complete in mat-stepper?

There doesn't seem to be a direct way to do this as per the docs. There is a completed and state input though which we can use on the final mat-step.

If you see the code for the stepper on GitHub, you can see the following condition

if (step._showError && step.hasError && !isCurrentStep) {
    return STEP_STATE.ERROR;
} else if (step.completed && !isCurrentStep) {
    return STEP_STATE.DONE;
} else if (step.completed && isCurrentStep) {
    return state;
}

This shows that setting completed alone is not sufficient since the final step will still be the current step. But as we can see from the condition, all we need to do now is change state as well.

In your last mat-step, add completed and state

<mat-step [completed]="completed" [state]="state">
    <ng-template matStepLabel>Done</ng-template>
        You are now done.
    <div>
        <button mat-button matStepperPrevious>Back</button>
        <button mat-button (click)="done()">Confirm</button>
    </div>
</mat-step>

Then control this in your component when the button is clicked.

completed: boolean = false;
state: string;

done() {
    this.completed = true;
    this.state = 'done';
    console.log(this.firstFormGroup.valid);
    console.log(this.secondFormGroup.valid);
}

Note: You can use the validity of the forms to conditionally set these two variables or show an error message to prompt the user to complete the rest of the steppers.

Here is a working example on StackBlitz.